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Estimating tail risk measures is an important task in many financial and actuarial applications and often requires nested simulations, with the outer simulations representing real world scenarios, and the inner simulations typically used for risk neutral pricing or conditional risk measurement. The standard nested simulation method is highly flexible, able to incorporate complex asset models and exotic payoff structures, but it is also computationally highly burdensome, particularly in a multi-period setting, when inner simulation paths are required at each time step of each outer level scenario. In this study, we propose and analyze a two-stage simulation procedure that efficiently estimates the conditional tail expectation of cost of a dynamic hedging program for a Variable Annuity Guaranteed Minimum Withdrawal Benefit (GMWB), under a multi-period nested simulation. In each of the two stages, the method re-uses the same set of inner level simulation paths for each outer scenario at each time point, using a likelihood ratio method to re-weight the probabilities of each individual path for the different outer scenarios. Our numerical study shows that our two-stage, likelihood ratio weighted procedure can offer a very significant improvement in efficiency, of the order of 95% as measured by the RMSE, compared with a standard nested simulation with the same computational cost. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada, funding reference number 03754 (Hardy) and 03755 (Feng). This work was also supported by the Society of Actuaries through a Center of Actuarial Excellence Research Grant and through the Hickman Scholarship held by Ou Dang. Ou Dang has also received support from the Ontario Graduate Scholarship.

Estimating tail risk measures for portfolios of complex variable annuities is an important enterprise risk management task which usually requires nested simulation. In the nested simulation, the outer simulation stage involves projecting scenarios of key risk factors under the real-world measure, while the inner simulations are used to value pay-offs under guarantees of varying complexity, under a risk-neutral measure. In this paper, we propose and analyse an efficient simulation approach that dynamically allocates the inner simulations to the specific outer scenarios that are most likely to generate larger losses. These scenarios are identified using a proxy calculation that is used only to rank the outer scenarios, not to estimate the tail risk measure directly. As the proxy ranking will not generally provide a perfect match to the true ranking of outer scenarios, we calculate a measure based on the concomitant of order statistics to test whether further tail scenarios are required to ensure, with given confidence, that the true tail scenarios are captured. This procedure, which we call the dynamic importance allocated nested simulation approach, automatically adjusts for the relationship between the proxy calculations and the true valuations and also signals when the proxy is not sufficiently accurate.

Target benefit (TB) plans that incorporate intergenerational risk sharing have been demonstrated to be welfare improving over the long term. However, there has been little discussion of the short-term benefits for members in a defined benefit (DB) plan that is transitioning to TB. In this paper, we adopt a two-step approach that is designed to ensure the long-term sustainability of the new plan, without unduly sacrificing the benefit security of current retirees. We propose a cohort-based transition plan for reducing intergenerational inequity. Our study is based on simulations using an economic scenario generator with some theoretical results under simplified settings.

This well-balanced introduction to enterprise risk management integrates quantitative and qualitative approaches and motivates key mathematical and statistical methods with abundant real-world cases - both successes and failures. Worked examples and end-of-chapter exercises support readers in consolidating what they learn. The mathematical level, which is suitable for graduate and senior undergraduate students in quantitative programs, is pitched to give readers a solid understanding of the concepts and principles involved, without diving too deeply into more complex theory. To reveal the connections between different topics, and their relevance to the real world, the presentation has a coherent narrative flow, from risk governance, through risk identification, risk modelling, and risk mitigation, capped off with holistic topics - regulation, behavioural biases, and crisis management - that influence the whole structure of ERM. The result is a text and reference that is ideal for graduate and senior undergraduate students, risk managers in industry, and anyone preparing for ERM actuarial exams.

The Wilkie economic scenario generator has had a significant influence on economic scenario generators since the first formal publication in 1986 by Wilkie. In this article we update the model parameters using U.S. data to 2014, and review the model performance. In particular, we consider stationarity assumptions, parameter stability, and structural breaks.

In this paper, we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, which has been offered to public employees in the state ...

In this paper, we discuss optimal design for stylized Intergenerational Risk Sharing (IRS) pension plans. We study an IRS plan under which both contributions and pension benefits are adjusted based on the level of pension assets. Our optimization focuses on the stability of members’ lifetime consumption, both in the contribution and benefit phases, through formulating the optimization as an ergodic control problem. We illustrate the drawbacks of unconstrained optimization and demonstrate the importance of including regulatory requirements for the sake of fairness across generations. In this formulation, the employers are not included; implicitly, it is assumed that employer contributions would be paid as salary to the workers if not required for the plan, so the employer risk is eliminated.

The financial guarantees embedded in variable annuity contracts expose insurers to a wide range of risks, lapse risk being one of them. When policyholders’ lapse behavior differs from the assumptions used to hedge variable annuity contracts, the effectiveness of dynamic hedging strategies can be significantly impaired. By studying how the fee structure and surrender charges affect surrender incentives, we obtain new theoretical results on the optimal surrender region and use them to design a marketable contract that is never optimal to lapse.

This paper provides an in-depth investigation of Epstein-Zin preferences under an uncertain lifetime. These models have been gaining popularity as normative preference models in life-cycle applications. Though extensively used, it is unclear if the preference models are well-understood by the users. To this end, this paper studies the decision-making under Epstein-Zin preferences. Specifically, analytical solutions for a simple consumption and savings problem are derived, isolating the impact of relative risk aversion (RRA), elasticity of intertemporal substitution (EIS), time discounting, and risks stemming from mortality, investment, and inflation. We investigate three Epstein-Zin preference models that differ in their treatment of mortality risk, and find that some lead to normatively implausible solutions. Importantly, we find that the EIS is not always monotone in its effect on consumption volatility over time, meaning that its interpretation can be ambiguous when considering an uncertain future lifetime. This has been misinterpreted in the literature to date. We also show that one particular Epstein-Zin specification is not necessarily a generalization of expected discounted utility maximization in the case of constant relative risk aversion, as many works wrongly claim.

Cash balance pension benefits are accumulated at guaranteed crediting rates, usually based on yields on government securities. Viewed as a financial liability, the benefit is a form of interest rate derivative, which can be valued using financial models and theory. In this article, we derive the market value for a range of commonly used crediting rates, assuming the accrued benefit liability comprises the past contributions, allowing for full interest credits up to a known future retirement date. We use the Hull-White interest rate model to determine crediting rates and to determine the market value. We explore the risks associated with different crediting rate choices by evaluating the liability using market data from 1998 to 2013. We propose two other approaches to the accrued benefit. The first approach assumes the accrued benefit comprises past contributions with interest up to the valuation date, but no future interest credits. Future credits on past contributions are assumed funded through future co...

This Special Issue of the North American Actuarial Journal contains 15 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the articles w...

Objective 7-Hydroxymaitairesinol (7-HMR) is a naturally occurring plant lignan found in whole grains and the Norway spruce (Piciea abies). The purpose of this study was to evaluate the bioavailability of a proprietary 7-HMR product (HMRlignan, Linnea SA, Locarno, Switzerland) through measurement of lignan metabolites and metabolic precursors. Methods A single-blind, parallel, pharmacokinetic and dose-comparison study was conducted on 22 post-menopausal females not receiving hormone replacement therapy. Subjects were enrolled in either a 36 mg/d (low-dose) or 72 mg/d dose (high-dose) regimen for 8 weeks. Primary measured outcomes included plasma levels of 7-HMR and enterolactone (ENL), and single-dose pharmacokinetic analysis was performed on a subset of subjects in the low-dose group. Safety data and adverse event reports were collected as well as data on hot flash frequency and severity. Results Pharmacokinetic studies demonstrated 7-HMR Cmax = 757.08 ng/ml at 1 hour and ENL Cmax = 4.8 ng/ml at 24 hours. From baseline to week 8, plasma 7-HMR levels increased by 191% in the low-dose group (p < 0.01) and by 1238% in the high-dose group (p < 0.05). Plasma ENL levels consistently increased as much as 157% from baseline in the low-dose group and 137% in the high-dose group. Additionally, the mean number of weekly hot flashes decreased by 50%, from 28.0/week to 14.3/week (p < 0.05) in the high-dose group. No significant safety issues were identified in this study. Conclusion The results demonstrate that HMRlignan is quickly absorbed into the plasma and is metabolized to ENL in healthy postmenopausal women. Clinically, the data demonstrate a statistically significant improvement in hot flash frequency. Doses up to 72 mg/d HMRlignan for 8 weeks were safe and well tolerated in this population.

For valuation of Variable Annuity contracts with a dynamic hedging program using Monte Carlo methods, nested simulation is often required. The process is computationally challenging, sometimes prohibitively so, in many practical applications. We propose a simulation procedure for estimating the Conditional Tail Expectation (CTE) of liabilities of a Variable Annuity dynamic hedging strategy. In a CTE calculation, tail scenarios, i.e., the scenarios that result in extreme losses, are most relevant. Thus, correctly identifying those scenarios would greatly improve the efficiency in a nested simulation. The proposed procedure takes advantage of the special structure of the CTE by first identifying a small set of potential tail scenarios from the first tier of simulation. We then focus the simulation budget on only those scenarios. We conduct extensive numerical experiments on different guarantee types and different stochastic stock return dynamics. The numerical results show that, when given a fixed simulation budget, the proposed procedure can improve the accuracy of CTE estimation by an order of magnitude compared to a standard nested simulation.

In this paper we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, which has been offered to public employees in the state of Florida since 2002. The state runs both defined contribution (DC) and defined benefit (DB) pension plans. Employees who initially join the DC plan have the option to convert to the (DB) plan at a time of their choosing. The cost of the switch is assessed in terms of the ABO (Accrued Benefit Obligation), which is the expected present value of the accrued DB pension at the time of the switch. If the ABO is greater than the DC account, the employee is required to fund the difference. The second is the DB Underpin option, also known as a floor offset plan, under which the employee participates in a DC plan, but with a guaranteed minimum benefit based on a traditional DB formula. The third option can be considered a variation on each of the first two. We remove the requirement from the FSE option for employees to fund any shortfall at the switching date. The resulting plan is similar to the DB underpin, but with the possibility of early exercise. We adopt an arbitrage-free pricing methodology to value each option. We analyse and value the optimal switching strategy for the employee by constructing an exercise frontier, and we illustrate numerically the difference between the FSE, DB Underpin and Early Exercise DB Underpin options.

The Wilkie economic scenario generator has had a significant influence on economic scenario generators (ESGs) since the first formal publication in Wilkie (1986). In this paper we update the model parameters using U.S.data to 2014, and review the model performance. In particular, we consider stationarity assumptions, parameter stability, and structural breaks.

Reverse mortgages provide a mechanism for seniors to release the equity that has been built up in their home. At termination, the mortgagors are usually guaranteed to owe no more than the value of their property. The value of the reverse mortgage guarantee is heavily dependent on the maturity or termination date, which is uncertain. In this paper, we model reverse mortgage terminations using a semi-Markov multiple state model which incorporates three different modes of exit: death, entrance into a long-term care facility, and voluntary prepayment. We apply the proposed model specifically to develop the valuation formulas for roll-up mortgages in the UK and Home Equity Conversion Mortgages (HECMs) in the USA. We examine the significance of each mode of termination by valuing the contracts allowing progressively for each mode. On the basis of our model and assumptions, we find that both health related terminations and voluntary (non-health related) terminations significantly impact the contract value. In addition we analyze the premium structure for US reverse mortgage insurance, and demonstrate that premiums appear to be too high for some borrowers, and substantial cross-subsidies may result.

Many insurance products provide benefits that are contingent on the combined survival status of two lives. To value such benefits accurately, we require a statistical model for the impact of the survivorship of one life on another. In this paper we first set up two models, one Markov and one semi-Markov, to model the dependence between the lifetimes of a husband and wife. From the models we can measure the extent of three types of dependence: (1) the instantaneous dependence due to a catastrophic event that affect both lives, (2) the short-term impact of spousal death, and (3) the long-term association between lifetimes. Then we apply the models to a set of jointlife and last-survivor annuity data from a large Canadian insurance company. Given the fitted models, we study the impact of dependence on annuity values and examine the potential inaccuracy in pricing if we assume lifetimes are independent. Finally, we compare our Markovian models with two copula models considered in previous research on...

In examining basis risk in index longevity hedges, it is important not to ignore the dependence between the population underlying the hedging instrument and the population being hedged. We consider four extensions to the Lee-Carter model that incorporate such dependence: Both populations are jointly driven by the same single time-varying index, the two populations are cointegrated, the populations depend on a common age factor, and there is an augmented common factor model in which a population-specific time-varying index is added to the common factor model with the property that it will tend toward a certain constant level over time. Using data from the female populations of Canada and the United States, we show the augmented common factor model is preferred in terms of both goodness-of-fit and ex post forecasting performance. This model is then used to quantify the basis risk in a longevity hedge of 65-year old Canadian females structured using a portfolio of q-forward contracts predicated on U...

Longevity improvements have contributed to widespread underfunding of pension plans and losses in insured annuity portfolios. Insurers might reasonably expect some upside from the effect of lower mortality on their life business. Although mortality improvement scales, such as the Society of Actuaries Scale AA, are widely employed in pension and annuity valuation, the derivation of these scales appears heuristic, leading to problems in deriving meaningful measures of uncertainty. We explore the evidence on mortality trends for the Canadian life insurance companies, data, using stochastic models. We use the more credible population data to benchmark the insured lives data. Finally, we derive a practical, model-based formula for actuaries to incorporate mortality improvement and the associated uncertainty into their calculations.

In a roll-up mortgage, the borrower receives a loan in the form of a lump sum. The loan is rolled up with interest until the borrower dies, sells the house, or moves into long-term care permanently. The house is sold at that time, and the proceeds are used to repay the loan and interest. Most roll-up mortgages are sold with a no-negative-equity guarantee (NNEG), which caps the redemption amount at the lesser of the face amount of the loan and the sale proceeds. The core of this study is to develop a framework for pricing and managing the risks of the NNEG.

In this paper the defined benefit underpin guarantee is valued as a financial option, within the traditional funding paradigms of actuarial science. Assuming fixed interest rates, and assuming that salaries can be treated as a tradable asset, we value the guarantee using fair value principles. Contribution rates are developed for the Entry Age Normal, Projected Unit Credit, and Traditional Unit Credit funding methods. In addition, for the accruals methods, we demonstrate the implied hedging strategy. The traditional unit credit offers the best method of these three, as it is consistent with the principles of financial economics, and the resulting contributions more naturally follow the cost of the emerging benefit, without creating expensive barriers to new hires. The method generates significant contribution volatility, and we demonstrate how this can be reduced with suitable benefit design and ongoing risk management.

In this paper we propose a new capital allocation method based on an idea of [Sherris, M., 2006. Solvency, capital allocation and fair rate of return in insurance. J. Risk Insurance 73 (1), 71–96]. The proposed method explicitly accommodates the notion of limited liability of the shareholders. We show how the allocated capital can be decomposed, so that each stakeholder can have a clearer understanding of their contribution. We also challenge the no undercut principle, one of the widely accepted allocation axioms, and assert that this axiom is merely a property that certain allocation methods may or may not meet.

Traditionally, actuaries have modeled mortality improvement using deterministic reduction factors, with little consideration of the associated uncertainty. As mortality improvement has become an increasingly significant source of financial risk, it has become important to measure the uncertainty in the forecasts. Probabilistic confidence intervals provided by the widely accepted Lee-Carter model are known to be excessively narrow, due primarily to the rigid structure of the model. In this paper, we relax the model structure by considering individual differences (heterogeneity) in each age-period cell. The proposed extension not only provides a better goodness-of-fit based on standard model selection criteria, but also ensures more conservative interval forecasts of central death rates and hence can better reflect the uncertainty entailed. We illustrate the results using US and Canadian mortality data.

In Kim and Hardy (2007) the exact bootstrap was used to estimate certain risk measures including Value at Risk and the Conditional Tail Expectation. In this paper we continue this work by deriving the influence function of the exact-bootstrapped quantile risk measure. We can use the influence function to estimate the variance of the exact-bootstrap risk measure. We then extend the result to the L-estimator class, which includes the conditional tail expectation risk measure. The resulting formula provides an alternative way to estimate the variance of the bootstrapped risk measures, or the whole L-estimator class in an analytic form. A simulation study shows that this new method is comparable to the ordinary resampling-based bootstrap method, with the advantages of an analytic approach.

The rapid emergence of centenarians has highlighted the importance of survival probabilities at extreme ages and has motivated actuaries to look for alternative ways to close of life tables in place of assigning a death probability of 1 at an arbitrarily chosen age. Using the asymptotic results of modern extreme value theory, we propose a model, which we call the threshold life table, to extrapolate survival distributions to extreme ages and to determine the appropriate end point of a life table. By combining the threshold life table with the Lee-Carter model for stochastic mortality forecasting, we consider applications to the valuation of a life annuity portfolio and to the prediction of the highest attained age. We illustrate the theoretical results using U.S., Canadian, and Japanese mortality data.

In this paper we explore the bias in the estimation of the Value at Risk and Conditional Tail Expectation risk measures using Monte Carlo simulation. We assess the use of bootstrap techniques to correct the bias for a number of different examples. In the case of the Conditional Tail Expectation, we show that application of the exact bootstrap can improve estimates, and we develop a practical guideline for assessing when to use the exact bootstrap.

A number of models have been proposed for the equity return process for equity-linked guarantees, following the introduction of stochastic modeling requirements by the Canadian Institute of Actuaries and the American Academy of Actuaries. In this paper we present some of the models that have become well known and discuss the use of residuals to test the fit. After showing that the use of the static, “actuarial approach” to risk management can result in two models with very similar likelihood and residuals giving very different capital requirements, we propose an extension of the bootstrap to compare all the models and to determine whether the optimistic or pessimistic view of the long-term left tail risk is more consistent with the data. Our context is the determination of capital requirements, so we are concerned in this work with real-world rather than riskneutral processes.

The authors analyze the pilot implementation of a statewide automated outcome monitoring system (OMS) in California, using the perspectives of substance abuse treatment providers responsible for its day-to-day operation. To gain a better understanding of changes experienced by staff and their perceptions of barriers and facilitators of implementation, they conducted 28 focus groups designed to inform midstream adjustments to the system prior to its possible roll-out. Qualitative analysis of the focus group data revealed five important factors influencing implementation: the treatment provider's ethos, the time-consuming nature of the OMS, staff buy-in, resources, and counselor and program discretion. Lessons learned underscored the importance of taking into consideration aspects of organizational change and institutional resources and infrastructure when implementing a major change such as an automated OMS. Findings might be useful to those designing and implementing similar systems or other large organizational change initiatives.

Objective This survey intended to clarify physicians' understanding of the issues surrounding women, menopause, alternative medicine, and drug therapy for the treatment of menopause. Study design This study was designed as a national probability sample survey of primary care physicians and gynecologists nationwide. Its focus was to identify major concerns and issues identified by patients about menopause and perceived communication with effectiveness how to communicate with their patients. Physicians were also asked to rate their comfort level in recommending the use of herbal remedies and which herbal remedy they felt comfortable recommending to interested patients. Results Data indicated that a patient's complaint about menopausal symptoms was the most common factor leading to discussion of menopausal issues with physicians (91%) and that the primary concern to the patient was management of menopausal symptoms. Other factors were controversies about hormone replacement therapy, long-term health implications of menopause, and hormone replacement therapy. Eighty percent of the physician found confusing messages with regard to menopause to be the most challenging aspect in patient communication. The second most challenging issue is "inconclusive data about hormone replacement therapy" (56%). Seventy-six percent of the physicians found "showing sympathy" to be the most important factor for the physicians to communicate effectively with patients, whereas "being honest and open" was the most important patient attitude cited for the same purpose. When it comes to herbal therapy for menopause symptom control, only 4% of the physicians indicated that none of their patients take any remedies. Only 18% were not very comfortable in discussing or recommending herbal therapies, whereas the rest ranged from fairly comfortable to completely comfortable. Conclusion This study has provided data with regard to physician understanding of menopause treatment options and their primary interaction with patients on this issue. More in-depth studies concerning efficacy and/or side effects of each available treatment will be the relevant next step, given the controversies about both hormone replacement therapy and alternative therapies. The relative efficacy, safety, and cost-effectiveness of different treatments should also be put into the context of both clinical diagnosis and physicians' clinical judgment. Attention to comments by physicians and patients with regard to communication may produce better information exchange and trust between patient and physician.

California's voter-initiated Substance Abuse and Crime Prevention Act (SACPA) mandated a large-scale criminal justice policy shift, offering community-based, court-monitored treatment for non-violent drug-involved adult offenders in lieu of incarceration. In this article, we analyze implementation issues that arose during SACPA's first year. Issues were identified in focus groups conducted with stakeholders in 10 counties. For the analysis we adapted Winter's [Winter, S. (1990). Integrating implementation research. In D. J. Palumbo & D. J. Calista (Eds.), Implementation and the policy process: Opening up the black box (pp. 19–38). New York: Greenwood Press] framework for studying policy implementation to focus on policy interpretation, target group behavior, agency and interagency implementation practices, and ‘street-level bureaucrats.’ Among the issues examined are: local control; drug court influences; high need clients; interagency communication and cooperation; filing and prosecution of cases; infusion of the therapeutic ethos; interagency assessment teams; monitoring and reporting; service delivery problems and solutions; insufficient resources; and staff workload and burnout.

In this paper we present a method for defining a dynamic risk measure from a static risk measure, by backwards iteration. We apply the method to the conditional tail expectation (CTE) risk measure to construct a new, dynamic risk measure, the iterated CTE (ICTE). We show that the ICTE is coherent, consistent, and relevant according to the definitions of Riedel (2003), and we derive formulae for the ICTE for the case where the loss process is lognormal. Finally, we demonstrate the practical implementation of the ICTE to an equity-linked insurance contract with maturity and death benefit guarantees.

Under a guaranteed annuity option, an insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970's and 1980's when long-term interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990's, as long-term interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred.The emerging liabilities under these guarantees threatened the solvency of some companies and led to the closure of Equitable Life (UK) to new business. In this paper we explore the pricing and risk management of these guarantees.

The financial guarantees embedded in variable annuity (VA) contracts expose insurers to a wide range of risks, lapse risk being one of them. When policyholders' lapse behavior differs from the assumptions used to hedge VA contracts, the effectiveness of dynamic hedging strategies can be significantly impaired. By studying how the fee structure and surrender charges affect surrender incentives, we obtain new theoretical results on the optimal surrender region and use them to design a marketable contract that is never optimal to lapse.

This paper describes how to apply Markov Chain Monte Carlo (MCMC) techniques to a regime switching model of the stock price process to generate a sample from the joint posterior distribution of the parameters of the model. The MCMC output can be used to generate a sample from the predictive distribution of losses from equity linked contracts, assuming first an actuarial approach to risk management and secondly a financial economics approach. The predictive distribution is used to show the effect of parameter uncertainty on risk management calculations. We also explore model uncertainty by assuming a GARCH model in place of the regime switching model. The results indicate that the financial economics approach to risk management is substantially more robust to parameter uncertainty and model uncertainty than the actuarial approach.

In this article, we discuss approximation methods for aggregate claims distributions. The methods discussed are the normal approximation; the translated gamma approximation; Bowers' gamma approximation; the normal power approximation; Haldane's method; the Wilson–Hilferty approximation and the Esscher approximation. Worked examples are included, using a compound Poisson distribution with Pareto secondary distribution. Keywords: aggregate claims distribution; normal approximation; translated gamma; normal power; Bowers' gamma method; Haldane's method

In this paper I first define the regime-switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the regime-switching model is derived. Prices of European options using the regime-switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the regime-switching lognormal model results with those using the more traditional lognormal stock return model.

Three methods for determining suitable provision for maturity guarantees for single-premium segregated fund contracts are compared. Actuarial reserving assumes funds are held in risk-free assets, to give a prescribed probability of meeting the guarantee liability. Dynamic hedging uses the Black-Scholes framework to determine the replicating portfolio. Static hedging assumes a counterparty is willing to sell the options required to meet the guarantee. Using a stochastic cash flow projection, we consider how to assess which approach is most profitable. The example given assumes a typical Canadian segregated fund contract.

We discuss the concept of the risk measure as an expectation using a probability distortion, and classify the standard risk measures according to their associated distortion functions. Using two examples, we explore the features of the different measures.

Bühlmann-Straub credibility is used to find an estimate of the mortality loss ratio for a company, relative to a standard table, for use in the statutory valuation of life insurance business. A method for calculating the margin for adverse deviation to be added to the mortality rate (in accordance with the general principle of Canadian statutory valuation) is derived. Applying credibility further to the variance of the mortality loss ratio gives a methodology for calculating the amount of the surplus (i.e. capital) required to cover annual fluctuations in mortality experience. The necessary structural parameters are calculated from industry statistics; the methodology is illustrated using Canadian life insurance data.

This paper examines the pricing of and reserving for certain guarantees that are associated with some insurance contracts. Specifically we deal with maturity guarantees, which provide a minimum level of benefits at contract maturity. Under these contracts the policyholders' premiums are invested in a specified portfolio. When the contract matures the value of the benefit is guaranteed not to fall below a certain level. We examine and contrast two approaches to the pricing and reserving for these guarantees. The first approach is based on stochastic simulation of future investment returns. The second approach is based on modern option pricing theory. The reserving procedures under the two approaches differ dramatically. We provide numerical estimates of the reserves required under each approach using realistic assumptions. We find that the conventional option hedging strategies in the presence of transaction costs become relatively expensive.

(2005). We Are All “Actuaries Of The Third Kind” Now. North American Actuarial Journal: Vol. 9, No. 2, pp. iii-v.