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We investigate the use of Bregman iteration method for the solution of the portfolio selection problem, both in the single and in the multi-period case. Our starting point is the classical Markowitz mean-variance model, properly extended to deal with the multi-period case. The constrained optimization problem at the core of the model is typically ill-conditioned, due to correlation between assets. We consider l1-regularization techniques to stabilize the solution process, since this has also relevant financial interpretations.

This paper deals with the problem of quantifying the longevity impact for defined contribution pension funds in a stochastic environment. In the accumulation phase it is well known that, in presence of a benefit guarantee, the investment risk dominates the demographic one. However, if the generic subscriber life expectancy increases, it is very likely that, in the decumulation phase, the wealth accrued will not be able to cover the liabilities of the fund. For this reason, the fund will be forced to set aside more resources in order to front its liabilities exposing itself to greater financial risk. In this paper we study the interaction between financial risk and longevity: based on the Italian experience for both financial and demographic factors, this work aims to measure the impact of longevity on the financial factor.

The use of a BEKK (Baba-Engle-Kraft-Kroner) model is proposed to estimate the volatility of a set of financial historical series with a view to the selection of a stock portfolio. An individual element on the diagonal of the volatility matrix is estimated by applying the model to the series of log returns both of the share i to which it refers and of the market index. An extra-diagonal element is instead estimated by using in the model the covariances between the series of log returns of the two shares i and j to which the element of the volatility matrix corresponds. The procedure proposed for the estimation of volatility was applied to the series of monthly stock log returns of 150 shares of major value traded on the Italian market between 1 January 1975 and 31 August 2011 and the Markowitz portfolio is simulated.

Pension funds have adopted different management approaches to overcome the arising difficulties to maintain a solid financial status. Among these, there is the adoption of an indexation policy which is conditional on the solvability of the fund. Pension funds recognizing conditional inflation indexation are obliged to pay an additional payoff linked to the inflation rate through some specific rule. The additional payoff normally takes the form of a contingent claim conditional to a measure of sustainability of the payoff itself; in most cases, the measure is linked to an asset/liability ratio able to capture the solvability of the fund. Therefore, a full valuation of the obligation towards funds participants cannot exclude the proper appraisal of this additional option. The option payoff is conditional to a measurement asset that is different from the reference underlying asset. This structure recalls a barrier option with different measurement and payoff asset. The paper investigates the opportunity to apply barrier option schemes in an asset/liability context to provide a full valuation of the obligation towards participants. Results derive from a simulation procedure applied by means of scenario-based analysis. Numerical results give the opportunity to state the absolute and relative value of the inflation option.

The paper deals with the solvency analysis through internal models in the case of a portfolio of life annuities, focusing on the interplay between stochastic interest rate dynamics and the survival evolution in time. This specific aspect is investigated basing the survival death rates on Poisson Lee Carter model approached according to the Iterative Procedure and two simulated approaches on the Poisson Lee Carter: the Standard Procedure and the Stratified Sampling Procedure. The financial aspect, particularly notable in portfolios with long duration and multiplicity of payments as in the considered case, is tackled assuming different stochastic hypotheses on the interest rates evolution. Aim of the paper is to deepen the reaction of solvency measures as the surplus index and the ruin probability to the specific financial and demographic scenario. The indexes are studied in different loading factor assumptions and several numerical applications illustrate the model setup.

The standard practice to predict economic behaviour has been to infer decision processes from the business cycle. Current decisions depend on the individual expectation of future variables including stock market returns, job loss, earning and social security benefit. Recently, several studies have looked at identifying how the effects of (subjective) perception affect the economic security of household well-being. After reviewing some preliminary concepts in this area, we implement a statistical model to analyse individual choices. We discuss properties and check their usefulness and consistency by means of data related to the Survey of Household Income and Wealth. An analysis of this model helps us understand individual uncertainty and how perception evolves over the life cycle conditioned by education and happiness. Some final remarks conclude the paper. © Springer-Verlag Italia 2012.

In this paper we extend the Least Squares Monte Carlo approach proposed by Longstaff and Schwartz for the valuation of American-style contingent-claims to the case of life insurance contracts. These contracts, in fact, often embed an American-style option, called surrender option, that entitles its owner to terminate early the contract and receive a cash amount, called surrender value. The additional complication arising in life insurance policies with respect to purely financial American contracts is that there is not a fixed date within which the option can be exercised, since its “maturity” is driven by mortality factors. This complication has been handled by very few papers, often at the cost of excessively simplified valuation frameworks. The aim of this contribution, that is not a specific valuation model but a methodological approach, is to allow a full exploitation of the flexibility inborn in Monte Carlo and quasi-Monte Carlo methods in order to deal with more realistic valuation frameworks.

This paper deals with the application of the Value at Risk of the mathematical provision within a fair valuation context. Through the VaR calculation, the estimate of an appropriate contingency reserve is connected to the predicted worst case additional cost, at a specific confidence level, projected over a fixed accounting period. The numerical complexity is approached by means of a simulation methodology, particularly suitable also in the case of a large number of risk factors.

Aim of the paper is the anlysis of riskiness in life insurance business by means of quantitative methodologies flexible for entrapreunerial applications. The study focuses on deferred life annuity portfolios, providingrisk indexes; however the results and the methodological approach presented can be framed in a wider perspective, where actuarial methodologies and business administration schemes sinergically investigate the insurance business scenarios.