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Results well known in the actuarial community about closed-form expressions to Gompertz and Gompertz-Makeham life expectancies for a person aged x are still being independently rediscovered to this day. This note seeks to acknowledge previous results about closed-form expressions to Gompertz-Makeham life expectancies, especially in the actuarial science field, hoping to stimulate interdisciplinarity and provide the background for further developments, especially since the derivation of closed-form expressions for life expectancy (and annuities) based on particular mortality laws are matters of interest for multiple fields such as actuarial science, biology, demography, statistics among others. Resumo Resultados bem conhecidos pela comunidade atuarial sobre expressões de forma fechada para esperança de vida de Gompertz e Gompertz-Makeham para uma pessoa de idade x ainda estão sendo redescobertos de forma independente nos dias atuais. Esta nota visa fornecer algum reconhecimento aos resultados anteriores sobre expressões de forma fechada para expectativa de vida de Gompertz e Gompertz-Makeham, especialmente no campo das ciências atuariais, na esperança de estimular a interdisciplinaridade e fornecer o pano de fundo para novos desenvolvimentos, em especial porque a derivação de expressões de forma fechadas para expectativa de vida (e anuidades) com base em leis de mortalidade despertam o interesse de várias áreas, como ciências atuariais, biologia, demografia, estatística, entre outras. Resumen Los resultados bien conocidos por la comunidad actuarial sobre las expresiones de forma cerrada de las esperanzas de vida de Gompertz y Gompertz-Makeham para una persona de edad x todavía se están redescubriendo de forma independiente en la actualidad. Esta nota pretende reconocer algunos resultados anteriores sobre expresiones cerradas para la esperanza de vida de Gompertz y Gompertz-Makeham, en especial en el campo de las ciencias actuariales, con la esperanza de fomentar la interdisciplinariedad y proporcionar el telón de fondo para futuros desarrollos, sobre todo desde que la derivación de expresiones cerradas para la esperanza de vida (y anualidades) basado en leyes de mortalidad despertó el interés de varias áreas, como las ciencias actuariales, biología, demografía, estadística, entre otras.

We adapt the design of four experimental studies on retirement decision-making and conduct replications with a larger online sample from the broader population. We replicate most of the main effects of the original studies. In particular, we confirm that consumption decisions are less efficient when subjects need to borrow from the future than when they need to save from the present. When subjects collect retirement benefits as lump sum instead of annuities, they choose to retire later, as suggested by the original study. We also confirm that savings are higher when they are incentivized with matching contributions than when incentivized with tax rebates. However, when faced with varying survival risks, subjects in our replication make only partial adjustments to spending paths when ambiguity is reduced. We also propose a further experimental research agenda in related topics and discuss practical issues on subject recruitment, attrition, and redesign of complex tasks.

The aim of this paper is to estimate the relative importance of annuities and transfers in Greek retirement benefits and to assess their impact on intergenerational and intragenerational equity. We analyse a large sample of private sector workers retiring in 2008. Adopting a longitudinal approach, we compute the net present value of contributions paid and benefits received by individuals over their life course. We define the difference between the two as the implicit transfer, which can be either positive or negative. Lifetime retirement benefits are calculated both according to the rules in place at the time of retirement, and after the spending cuts introduced in 2010-2013. Our findings suggest that for the vast majority of retirees pension benefits are heavily subsidized, i.e. exceed the actuarially fair level paid for by social contributions. Austerity policies have reduced but not eliminated this subsidy.

This paper employs data from an original survey to analyse the annuity preferences of members of the Slovak-funded private pension pillar. The focus is on the impact of socioeconomic variables as well as various behavioural attitudes upon annuitisation decisions. The research first considers some well-known behavioural factors (framing, mental accounting) and then turns to some underresearched traits (indulgence, self-control) and behaviours (compulsive shopping, saving habits) and links them to annuity choices. Moreover, the research studies alternative allocations of a lump sum and relates them to annuitisation decisions. Indulgence emerged as a significant negative predictor of annuitisation. This result likely refers to preferences towards hedonic lifestyles in early retirement. Interestingly, low self-discipline was also significant but positively related to an intention towards annuity purchases. People who are aware of their low financial discipline may introduce internal self-protection mechanisms and resort to tried and tested financial products to avoid anticipated feelings of regret and desperation. Annuitisation, in this case, is a regret avoidance behaviour.

Des del Pla de Desenvolupament Econòmic de Sant Andreu presenten un petit resum de l’informe de diagnosi anual 2019 sobre la realitat socioeconòmica del Districte.

Artykuł poświęcony jest ryzyku długowieczności, a w szczególności wskazaniu jego wpływu na świadczenia rentowe wypłacane z ubezpieczeń odpowiedzialności cywilnej. Zjawisko wydłużania się życia jest obserwowane w ostatnich latach w krajach europejskich. Ma ono wpływ na wiele obszarów życia i gospodarki, a także dla finansów i ubezpieczeń. Zwiększający się udział osób starszych w społeczeństwie jest istotnym wyzwaniem tak dla państw, jak i instytucji finansowych, głównie banków, zakładów ubezpieczeń oraz funduszy hipotecznych. Podmioty te będą musiały uwzględniać wydłużanie się trwania życia w zarządzaniu systemami emerytalnymi oraz portfelem oferowanych produktów, w szczególności tych, które narażone są właśnie na ryzyko długowieczności z uwagi na płatności okresowe bez zakreślenia horyzontu czasowego. Przy niektórych produktach, jak odwrócona hipoteka czy renty z zamkniętym okresem płatności ryzyko właściwej oceny okresu wypłaty ciążyć będzie na beneficjencie. Świadome faktu wydłużania się życia muszą też osoby gromadzące swój kapitał emerytalny. W artykule autorki wskazują dane obrazujące zjawisko wydłużania trwania życia oraz ilustrują problem wpływu zjawiska w obszarze ubezpieczeń poprzez weryfikację znaczenia tego czynnika w kształtowaniu płatności rentowych w ubezpieczeniach OC. Ilustracje liczbowe ukazują wpływ wydłużania się dalszego trwania życia na obecną wartość kapitału rentowego oraz tego, jak przy utrzymaniu stałej wysokości minimalnej sumy gwarancyjnej obniża się wysokość kapitału na poczet miesięcznego świadczenia. The article discusses the longevity risk, in particular the indication of annuities paid under liability insurance. Extending life is observed in recent years in European countries. It has an impact on many areas of life and economy, as well as finance and insurance. The increasing number of older people in society is a major challenge both for the states and financial institutions, mainly banks, insurance companies and mortgage funds. These entities will also have to consider lengthening life expectancy in the management of pension systems and the portfolio of products offered, in particular those exposed to longevity risk just because of the payments without final time horizon. The risk of lengthening of life is also important for future retirees and affects size of adequate pension capital. In the article the authors picture the phenomenon of lengthening life time and next illustrate the impact on annuities paid for bodily injuries under liability insurance.

The transition from defined benefit to defined contribution (DC) pension schemes has raised concern about whether retirees will have adequate income for their retirement. Prior literature has studied the optimal investment strategies for DC funds that provide minimum guarantees. But far less attention is paid to portfolio insurance strategies, despite their suitability to pension funds and their optimality to certain investors. This thesis evaluates the performance of option-based and constant proportion portfolio insurance strategies. They are implemented to a DC fund that targets an inflation- and longevity-protected annuity at retirement. The results show that both strategies provide strong protection against downside risk. In addition to occupational pension, housing is another important source of retirement savings. For young people entering the work force, home property purchase can significantly affect their savings for retirement. Literature on housing tenure choice largely focuses on determinants of home ownership, while its impact on retirement planning is rarely explored. This thesis investigates the question of when to become a homeowner from the perspective of financing retirement and conducts a welfare analysis. The presence of home equity can also affect individual demand for retirement products, such as annuities and long-term care insurance (LTCI). Despite high home ownership rates among retirees and significance of housing wealth in retired homeowners' portfolios, housing is often excluded from the literature of optimal consumption and portfolio choice. This thesis explains how homeowners' demand for annuities and LTCI differ from that of non-homeowners. Individuals have heterogeneous levels of risk aversion and willingness to substitute consumption over time, as measured by elasticity of intertemporal substitution (EIS). LTCI insures against uncertain healthcare costs, so retirees of higher risk aversion will demand more coverage. Annuities smooth consumption over time while providing longevity insurance, so EIS is potentially the chief determinant of optimal annuitisation rate. Existing research exploring demand for retirement products mostly uses a power utility function that imposes risk aversion is the reciprocal of EIS, reflecting preference of only a small group of retirees. This thesis extends the literature by separating these two factors and showing their different impact on demand for annuities and LTCI.

It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies, if the mortality force is a generic function of time and if the `subjective' life expectancy of the investor differs from the `objective' one adopted by insurance companies to price annuities. In this paper we address this problem considering an individual who invests in a fund and has the option to convert the fund's value into an annuity at any time. We formulate the problem as a real option and perform a detailed probabilistic study of the optimal stopping boundary. Due to the generic time-dependence of the mortality force, our optimal stopping problem requires new solution methods to deal with non-monotonic optimal boundaries., Comment: 34 pages, 5 figures; improved exposition

The use of lifetime annuities is one obvious candidate to deliver guaranteed income in retirement. This paper quantifies the marginal increase in income to a single male when compelled to purchase a lifetime annuity from superannuation savings, compared to the current position of voluntary annuitisation in the Australian market. It is found that significant increases in average income are possible under compulsion, with an associated decrease in the cost of the age pension. Future mortality is shown to be the key area of sensitivity. The critical importance of future age pension eligibility rules being adaptable in line with mortality changes is demonstrated.

This study utilizes a nationally representative proprietary dataset to examine the annuitization decisions of retirees. The results indicate that consulting a financial advisor, retirement duration, and risk aversion are positive predictors of annuity ownership. The results also indicate that retirees with defined benefit plans are more likely to own annuities. Additionally, the results suggest that households with retirement duration of ten years or longer are more likely to start receiving their annuity distributions. This paper contributes to the research on annuitization decisions of retirees. The unique contributions of our study include establishing the relationship between risk aversion, financial advice, and annuity ownership decisions of households using a nationally representative dataset. Our empirical model controls for a number of socioeconomic, demographic and income related variables that have been drawn from prior literature.

We develop a demographic macroeconomic model that captures the salient life-cycle features at the individual level and, at the same time, allows us to pinpoint the main mechanisms at play at the aggregate level. At the individual level the model features both age-dependent mortality and productivity and allows for less-than-perfect annuity markets. At the aggregate level the model gives rise to single-sector endogenous growth and includes a Pay-As-You-Go pension system. We show that ageing generally promotes economic growth due to a strong savings response. Under a defined benefit system the growth effect is still positive but lower than under a defined contribution system. Surprisingly, we find that an increase in the retirement age dampens the economic growth expansion following a longevity shock.

We develop a pair of risk measures, health and mortality delta, for the universe of life and health insurance products. A life-cycle model of insurance choice simplifies to replicating the optimal health and mortality delta through a portfolio of insurance products. We estimate the model to explain the observed variation in health and mortality delta implied by the ownership of life insurance, annuities including private pensions, and long-term care insurance in the Health and Retirement Study. For the median household aged 51 to 57, the lifetime welfare cost of market incompleteness and suboptimal choice is 3.2% of total wealth.

Good news can involve difficult decisions. For example winning a lottery jackpot can go along with the decision, whether to have the jackpot paid out immediately as a lump sum or as periodic annual payments. Also when entering retirement most people face the decision whether they want their defined contribution account balance paid as a lump sum or to annuitize that amount. The fact that people tend to choose the lump sum even if economic reasons suggest that they should choose the annuity is called the annuity paradox. In a large online survey we find that people behave time inconsistent: older people have a stronger tendency to choose the lump sum than younger people when they are asked to predict today what to choose when they retire. This effect is considerably stronger for participants that answer simple time preference questions inconsistently. Our findings suggest to think about precommitment devices for the annuitization decision, in the retirement case, already at the time when the defined benefit plan is started.

The paper examines the optimal annuitization time and the optimal consumption/investment strategies for a retired individual subject to a constant force of mortality in an all-or-nothing framework. We allow for a different utility of consumption before and after annuitization. For a general family of preferences we characterize the value function and the optimal controls of the resulting combined stochastic control and optimal stopping problem. Assuming power utility functions we obtain explicit solutions. We show that if the individual evaluates the consumption flow and the annuity payments stream in the same way, then, depending on the parameters of the economy, the annuity is purchased at retirement or never. In the case when the individual is more risk averse in the annuity assessment, it is optimal to defer the annuitization until her wealth reaches a threshold, and such threshold depends on the parameters of the economy.

Life insurance has become an increasingly important part of the financial sector over the past 40 years, providing a range of financial services for consumers and becoming a major source of investment in the capital market. But what drives the large variation in life insurance consumption across countries remains unclear. Using a panel with data aggregated at different frequencies for 68 economies in 1961-2000, this article finds that economic indicators such as inflation, income per capita, and banking sector development and religious and institutional indicators are the most robust predictors of the use of life insurance. Education, life expectancy, the young dependency ratio, and the size of the social security system appear to have no robust association with life insurance consumption. The results highlight the importance of price stability and banking sector development in fully realizing the savings and investment functions of life insurance in an economy.

Individuals in defined-contribution retirement funds currently have a number of options as to how to finance their post-retirement spending. The paper considers the ranking of selected annuitisation strategies by the probability of ruin and by expected discounted utility under different scenarios. ‘Ruin’ is defined as occurring when income falls below a given threshold, but does not relate to the extent of that deficit. If there is insufficient money to buy an inflation-linked annuity at retirement, then the minimisation of the probability of ruin tends to result in living annuities with a high equity content. This is because the objective function does not reflect the extent of shortfall of income or the investor’s level of risk aversion. The authors argue that this is a limitation to using the minimisation of the probability of ruin. Expected discounted utility may be more difficult to apply in practice, because of the complexity of explaining the approach to investors and the need to estimate a greater number of parameters explicitly. The authors argue that the use of expected discounted utility is, however, likely to be more representative of most investors’ perception of risk, and illustrate its use by applying an extended discounted utility model that caters for the bequest motive and different reference income levels.Keywords: Annuities; income drawdown; ruin theory; discounted utility

This paper studies the effects of health shocks on the demand for health insurance and annuities, precautionary saving, and the welfare implications of public policies in a simple life-cycle model. I show that when the health shock simultaneously increases health expenses and reduces longevity, the following results can be obtained via closed-form solutions. First, utility-maximizing agents would neither fully insure their uncertain health expenses nor fully annuitize their wealth, even in the absence of market frictions and bequest motives. Second, the effect of uncertain health expenses on precautionary saving may be smaller than what has been found in previous studies. Under certain conditions, uncertain health expenses may even reduce precautionary saving. Third, mandatory health insurance (e.g. public health insurance) tends to benefit the poor more, while mandatory annuitization (e.g. public pension) is more likely to favor the rich. A simple numerical application of the model to the US long term care (LTC) insurance market suggests that the simultaneous effect of health shock on health expenses and longevity is a quantitatively important reason why agents (especially the rich) do not purchase more private LTC insurance.

During the financial crisis, life insurers sold long-term insurance policies at firesale prices. In January 2009, the average markup, relative to actuarial value, was $-25$ percent for 30-year term annuities as well as life annuities and $-52$ percent for universal life insurance. This extraordinary pricing behavior was a consequence of financial frictions and statutory reserve regulation that allowed life insurers to record far less than a dollar of reserve per dollar of future insurance liability. Using exogenous variation in required reserves across different types of policies, we identify the shadow cost of financial frictions for life insurers. The shadow cost of raising a dollar of excess reserve was nearly \$5 for the average insurance company in January 2009.

The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIBOR model and aim at developing accurate and efficient log-Lévy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps and swaptions show that the approximations perform very well. In addition, we also consider the log-Lévy approximation of annuities, which offers good approximations for high volatility regimes.

Retirement security for Americans is one of the most critical public policy and personal financial issues and will be for decades in the future. Individuals that retire today can live an additional 30 or even 40 years with less secure income as corporations shift to defined contribution plans to fund retirement. Based on the life cycle savings hypothesis, immediate annuities should be appealing to retirees because they insure against the risks of outliving retirement assets by converting funds into a lifelong stream of income. However, research has found that retirees are reluctant to annuitize their wealth. This study examined the attitudes of Utah State University employees toward annuitization of retirement assets and explored the relationship between employee characteristics and their attitudes toward immediate annuities. Data for this study were collected through an online questionnaire emailed to Utah State University employees who participate in a defined contribution plan. The survey gathered information on retirement portfolio losses, expected longevity, financial confidence, familiarity with annuities, and attitudes toward immediate annuities. A total of 744 individuals answered the survey for a response rate of 43.2%. Based on the results of independent t tests, there were statistically significant differences between the attitudes of women and men toward immediate annuities. Women held more positive attitudes toward immediate annuities than men, and women who had taken a retirement planning class had more positive attitudes than women who had not attended a retirement class. In contrast, men who had attended a retirement class expressed less positive attitudes toward immediate annuities than men who had not. Male overconfidence in their investment knowledge and skills may explain this finding. A Pearson correlation coefficient revealed a negative correlation between risk aversion and attitudes toward annuities. As investment risk tolerance decreases, attitudes toward immediate annuities become more positive. An analysis of variance found that individuals with longer than average life expectancies had more positive attitudes toward immediate annuities than subjects with shorter than average life expectancies. Surprisingly, individuals who claimed to be most familiar with immediate annuities showed the least positive attitudes toward annuities. Income and assets, marital status, and financial confidence were not statistically significantly related to attitudes toward annuities. Implications for consumers, financial professionals, educators, and policymakers were drawn from the results of the study.

This paper examines how behavioural economics can be used to improve the expenditure decisions of retirees. It identifies how accumulated assets can be used optimally throughout retirement to produce life-long income when required, to make provision for contingencies – such as unanticipated spikes in expenditure – and to optimize the size and timing of bequests. We do this using a SPEEDOMETER (or Spending Optimally Throughout Retirement) retirement expenditure plan which employs defaults within a choice architecture. At its simplest, the plan involves just four key behavioural nudges: (1) First, make a plan – ideally with, but if necessary without, an adviser; (2) automatic phasing of annuitization which is designed to tackle the aversion to large irreversible transactions and losing control of assets and so allows the greatest possible degree of flexibility in managing the run-down of retirement assets; (3) capital protection in the form of ‘money-back’ annuities which deals with loss aversion, i.e., the fear of losing your money if you die early; and (4) the slogan ‘spend more today’ which utilizes hyperbolic discounting to satisfy the human trait of wanting jam today and to reinforce the idea that ‘buying an annuity is a smart thing to do’.

Campbell (2006) stressed the two main challenges of household finance: empirical analyses that highlight how households do invest (i.e. positive household finance) have important measurement problems, while suggestions about how investments should be made (i.e. normative household finance) encounter modelling problems. In this latter connection the final aim of this paper is to highlight the modelling requirements necessary to analyse the impact of household-specific risks on their portfolios, with special focus on the financial segment. To this end, after an overview of household portfolio theory, special emphasis is given to models incorporating two increasingly more important risks for the household: labour income and longevity risks. The paper concludes with some research directions.

The present paper Studies the growth and efficiency consequences of pension funding with individual retirement accounts in a general equilibrium overlapping generations model with idiosyncratic lifespan and labor income uncertainty. We distinguish between economies with rational and hyperbolic consumers and compare the consequences of voluntary and mandatory retirement plans. Three major findings are derived in our study: First, we quantify the commitment effect of social security for myopic individuals by roughly 1 percent of aggregate resources. It is possible to recapture this commitment technology in IRAs, if those are annuitized. Second, despite the fact that our consumers have an operative bequest motive, the welfare gain from the (implicit) longevity insurance of the pension system is significant and amounts to roughly 0.5 percent of aggregate resources. However, mandatory annuitization reduces unintended bequests so that future generations are significantly hurt. Finally, our results highlight the importance of liquidity effects for social security analysis. These efficiency gains are only attainable if accounts are voluntary and not mandatory.

Using microeconomic data for the United Kingdom, we analyze the empirical determinants of voluntary annuity market demand. We find that annuity market participation increases with financial wealth, life expectancy, and education and decreases with other pension income and a possible bequest motive for surviving spouses. We then show that these empirically motivated determinants of annuity market participation have the same, quantitatively important, effects in a life-cycle model of annuity and life insurance demand, saving, and portfolio choice. Moreover, reasonable preference parameters predict annuity demand levels comparable to the data. For stockholders, a strong bequest motive can simultaneously generate balanced portfolios and low annuity demand. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

This paper is aimed to answer a set of questions through an examination of the literature and empirical evidence on annuities. Every section of the paper try to address one specific question, naming: How important is the ageing problem in the world? How is social security being replaced or complemented by savings? What financial products provide financial safety for the elderly? Why the annuities market is so thin? Why the annuities market only develop when there is a mandate to annuitisize? How is Spanish annuity market organized? What regulatory issues are to be develop in order to expand the instrument? What reforms can be instrumented in Spain to expand the market?

Life annuities provide a guaranteed income for the remainder of the recipient’s lifetime, and therefore, annuitization presents an important option when choosing an adequate investment strategy for the retirement ages. While there are numerous research articles studying annuities from a pensioner’s point of view, thus far there have been few contributions considering annuities from the provider’s perspective. In particular, to date there are no surveys of the general risks within annuity books. The present paper aims at filling this gap: Using a simulation framework, it provides a long-term analysis of the risks within annuity books. In particular, the joint impact of mortality risks and investment risks as well as their respective influences on the insurer’s financial situation are studied. The key finding is that, under the model specifications and using annuity data from the United Kingdom, the risk premium charged for aggregate mortality risk seems to be very large relative to its characteristics. Possible reasons as well as economic implications are provided, and potential caveats are discussed.

This thesis explores the economic issues associated with the payout phase where a defined contribution (DC) retirement arrangement is adopted. In particular, the role of annuities in providing a retirement income is examined as well as insurance they provide against retirement risks such as inflation, longevity and rate of return volatility. A comprehensive money’s worth calculation based on a Australian population cohort mortality table shows that overall, Australian nominal and inflation indexed life annuities provide relatively good value for money. Although relative to annuities sold in the US and the UK they do suffer from relatively high adverse selection costs, which could in turn reduce demand. In addition, the presence of a government provided safety net pension could also result in low demand for annuities. These two issues suggest that government intervention may be warranted to ensure retirees have access to affordable private insurance to protect their retirement benefit. This could take the form of mandating an annuity purchase at retirement. However, which annuity should be mandated is not well understood. This is an important question as there are many alternative annuity designs, each providing different degrees of retirement risk protection to an individual. This thesis uses numerical simulations to empirically analyse the costs and benefits of mandating alternative annuities from both an individual and government’s perspectives to determine optimal annuity design. A model is used to estimate the value of payouts over time from various types of annuities across a range of retirement benefits. A means tested safety net pension is assumed to exist. Two stochastic variables — inflation and the risky rate of return, are simultaneously used to show how the annuity payouts react to theses changes, highlighting the insurance features of various annuities. Consumer preferences for the various annuities are estimated based on tolerance to risk. The variable annuity dominates the utility rankings under two conditions: -- when the relative risk aversion is low and a safety net payment isn’t available, and when the relative risk aversion is high and a safety net payment is made. Otherwise the CPI indexed annuity has the highest ranking. Sensitivity analysis shows that the results presented here are robust to a number of alternative assumptions about the key variables.

Regular annuities provide payment for the duration of an owner's life-time. Period-Certain annuities provide additional payment after death to adesignated beneficiary provided the insured dies within a certain period after annuitization. It has been argued that the bequest option offered by the latter is dominated by life insurance which provides non-random bequests. This is correct if competitive annuity suppliers have full information about individual longevities and price annuities accordingly. In contrast, this paper shows that when individual longevities are private information, a competitive pooling equi-librium which offers annuities at common prices to all individuals may have positive amounts of both types of annuities in addition to life insurance. In this equilibrium, individuals self-select the types of annuities that they purchase according to their longevity prospects. The break-even price of each type of annuity reflects the average longevity of its buyers plus expected lump-sum payouts in the case of period-certain annuities. The broad conclusion that emerges from this paper is that adverse-selection due to asymmetric information is reflected not only in the amounts of insurance purchased but,importantly, also in the choice of insurance products suitable for different individual characteristics. This conclusion is supported by recent empirical work about the UK annuity market (Finkelstein and Poterba (2004)).

Annuity premiums are often assumed to be constant, although they can be expected to vary with the yield curve. Variations in premiums will become an important public policy issue as defined-contribution (DC) pension plans play an increasingly prominent role in providing retirement income. As DC plan holders retire, many will annuitize at least a part of their account balances. In the absence of current data on annuity prices, the paper relies on U.S. Treasury interest rate data to simulate the impact of interest rate variation on annuity premiums. For a spectrum of feasible interest rates, the variation in retirement income is not negligible.

The Navy has several tools at its disposal to shape the force, including early separation incentives. This analysis looks at the issues surrounding the separation incentives including the discount rate for government use, the discount rate used by individuals to make a decision (personal discount rate), comparable civilian sector wages for separating personnel, promotion probabilities, and the costs to the government of maintaining personnel until retirement. Using the information provided from researching these topics, a model was created to identify the present value of retirement payments for officers given their current rank, age, and years of service. The model provided a maximum amount the government should be willing to offer to separate an officer early. This model was compared to a second model which determined the minimum amount an officer would be willing to accept to separate before retirement. Recommendations for future methods of shaping the force were provided to maximize savings to the Navy based on data generated from the model. http://archive.org/details/analysisofearlys109451236 Captain, United States Marine Corps Approved for public release; distribution is unlimited.

This paper solves an empirically parameterized model of households’ optimal demand for nominal and inflation indexed annuities. The model incorporates mortality, inflation, and real interest rate risk. The model draws some interesting predictions. First, the welfare calculations on the access to annuities markets show that nominal annuities are welfare improving even when sold at the empirically parameterized cost, which is above fair value. Real annuities are welfare improving over nominal annuities when sold at a fair price, but when we incorporate the empirically parameterized annuity premium the gains become negative at all wealth levels. Second, the simulation of the model for the British population wealth distribution shows that an important explanation for the little interest in annuities comes from the fact that annuities are extremely expensive, compared with the total accumulated assets held by households. In other words many households can not afford even to enter the annuity market. The paper also compares the simulated annuity demand to the actual demands reported in the Family Resources Survey. For those individuals who buy annuities, the simulated demands are not very different from those observed in the survey.

This paper constructs a time series of annuity rates in the UK for 1957-2002, and examines the pricing of UK annuities, and the relationship between the accumulation and decumulation phases of a defined contribution pension scheme by focusing on the properties of the pension replacement ratio. Using data on annuity returns and the returns on other financial assets, the paper simulates replacement ratios, to build up a frequency distribution of the pension replacement ratio for a UK individual. These frequency distributions illustrate the risk in the pension replacement ratio faced by an individual who saves in a typical defined contribution pension scheme.

Some researchers have raised concerns about significant volatility in initial payments from fixed immediate life annuities and the subsequent inflation risk during the retirement period. This paper investigates these concerns using recent high frequency data. It finds that while there is significant volatility in initial payments from nominal fixed annuities, phased purchases of fixed annuities can reduce their volatility. It also finds that an inflation-adjusted annuity may address both the volatility and inflation risk problems. The results are applicable to current discussions about Social Security and trends toward the defined contribution type of pension plan.

This Paper uses stochastic simulations on calibrated models to assess the steady state impact of different pension arrangements in an environment where financial markets are less than perfect. Surprisingly little is known about the optimal split between funded and unfunded systems when there are sources of uninsurable risk that are allocated in different ways by different types of pension system and where there are imperfections in financial markets (eg transaction costs or adverse selection). This Paper calculates the expected welfare of agents in different economies where in the steady state the importance of unfunded state pensions differs. We estimate how the optimal level of unfunded state pensions depends on rate of return and income risks and also upon the actuarial fairness of annuity contracts. We focus on the case of Japan where ageing is rapid and unfunded pensions are currently generous.

This paper uses stochastic simulations on calibrated models to assess the steady state impact of different pension arrangements in an environment where financial markets are less than perfect. Surprisingly little is known about the optimal split between funded and unfunded systems when there are sources of uninsurable risk that are allocated in different ways by different types of pension system and where there are imperfections in financial markets (eg transactions costs or adverse selection) . This paper calculates the expected welfare of agents in different economies where in the steady state the importance of unfunded, state pensions differs. We estimate how the optimal level of unfunded, state pensions depends on rate of return and income risks and also upon the actuarial fairness of annuity contracts. We focus on the case of Japan where aging is rapid and unfunded pensions are currently generous.

This paper uses stochastic simulations on calibrated models to assess the optimal degree of reliance on funded pensions and on a particular type of unfunded (PAYG) pension. Surprisingly little is known about the optimal split between funded and unfunded systems when there are sources of uninsurable risk that are allocated in different ways by different types of pension system. This paper calculates the expected welfare of agents in different economies where in the steady state the importance of PAYG pensions differs. We estimate how the optimal level of unfunded, state pensions depends on rate of return and income risks and also upon the actuarial fairness of annuity contracts.

The author examines the law regarding tax treatment of promises to pay in the future and finds it in a state of confusion. After discussing the inequities arising from the differing treatment accorded cash and accrual basis taxpayers the author suggests a number of changes in the tax treatment of installment sales and annuities given in exchange for property. The author also makes suggestions for simplification of the concept of cash equivalence