On approximate methods for the valuation of Life Assurances

Abstract

The question of the practical manner of proceeding in the valuation of a Life Insurance Company has become of increased importance by the introduction of Select Mortality Tables. Within the limits of a short lecture it is not possible to deal with all the valuable work that has been carried out in connection with this subject. Some very interesting suggestions have been put forward by Swedish Actuaries but these have, in the first place, been communicated to this Society.     

The benefits of a partnership approach to disability management

Taking a partnership approach to disability management and fostering a return-to-work culture can significantly reduce disability costs for employers and help disabled employees successfully return to work. Two rehabilitation case managers from ReliaStar Life Insurance Company share their perspective and experience, including three case studies that illustrate successful case management intervention and return-to-work strategies.     

An analytic valuation formula for unprotected American call options on stocks with known dividends

Sometimes it pays to exercise an American-type call option prematurely, just prior to a cash emission by the underlying security. Such an option can be expressed as a combination of three European-type options whose valuation formulae are known.     

A note on an analytical valuation formula for unprotected American call options on stocks with known dividends

This note provides simple analytic formulas for the value of an American call option on a stock with known dividends.     

The evolution of pay premiums for managerial attributes

This paper proposes and estimates an interactive fixed effects model of executive compensation, which allows for time-variant pay premiums for unobserved manager attributes. We find that two managerial traits can explain executive compensation over time: talent and conservatism. The market premium for talent is higher in bull markets, as the higher marginal productivity of human capital during these periods increases the demand and thus the price for talents. Such pay premium is concentrated among top talented managers, who earn a premium about five times that of median talented managers. The pay premium for conservatism is linked to the equity market risk premium, with conservatism being discounted (compensated) during the low (high) risk premium periods. We show that risk-taking managers are rewarded during the early period of our sample. However, after the periods characterized by higher risk premium, such as the financial crisis, conservatism becomes a more desirable trait.     

Kernel-type estimators for the distortion risk premiums of heavy-tailed distributions

A new kernel-type estimator for the distortion risk premiums of heavy-tailed losses is introduced. Using a least-squares approach, a bias-reduced version of this estimator is proposed. Under suitable assumptions, the asymptotic normality of the given estimators is established. A small simulation study, to illustrate the performance of our method, is carried out.     

Dynamic equilibrium and the structure of premiums in a reinsurance market

In this paper we present an economic equilibrium analysis of a reinsurance market. The continuous-time model contains the principal components of uncertainty; about the time instants at which accidents take place, and about claim sizes given that accidents have occurred. We give sufficient conditions on preferences for a general equilibrium to exist, with a Pareto optimal allocation, and derive the premium functional via a representative agent pricing theory. The marginal utility process of the reinsurance market is represented by the density process for random measures, which opens up for numerous applications to premium calculations, some of which are presented in the last section. The Hamilton-Jacobi-Bellman equations of individual dynamic optimization are established for proportional treaties, and the term structure of interest rates is found in this reinsurance syndicate. The paper attempts to reach a synthesis between the classical actuarial risk theory of insurance, in which virtually no economic reasoning takes place but where the net reserve is represented by a stochastic process, and the theory of equilibrium price formation at the heart of the economics of uncertainty.     

The benefits of a right to silence for the innocent

This article shows that innocent suspects benefit from exercising their right to silence during criminal proceedings. We present a model in which a criminal suspect can either make a statement or remain silent during police interrogation. At trial, the jury observes informative but imperfect signals about the suspect's guilt and the truthfulness of the suspect's statement. We show that a right to silence benefits innocent suspects by providing them with a safer alternative to speech, as well as by reducing the probability of wrongful conviction for suspects who remain silent with and without a right to silence.     

Some problems connected with the calculation of stop loss premiums for large portfolios

Abstract

Experience will not, as a rule, be sufficient to permit a direct empirical determination of the premium rates of a Stop Loss Cover when the portfolio to be reinsured is a large one, and when the treaty runs on such terms that there is only a small probability of the total amount of claims exceeding a stipulated limit. In such cases we have to fall back upon mathematical models from the theory of probability—especially the collective theory of risk—and upon such assumptions as—insofar as they cannot be empirically grounded —may be considered reasonable with regard to the nature of the problem.     

The valuation of warrants: Implementing a new approach

The option pricing model developed by Black and Scholes and extended by Merton gives rise to partial differential equations governing the value of an option. When the underlying stock pays no dividends – and in some very restrictive cases when it does – a closed form solution to the differential equation subject to the appropriate boundary conditions, has been obtained. But, in some relevant cases such as the one in which the stock pays discrete dividends, no closed form solution has been found. This paper shows how to solve these equations by numerical methods. In addition, the optimal strategy for exercising American options is derived. A numerical illustration of the procedure is also presented.     

Confined exponential approximations for the valuation of American options

We provide an alternative analytic approximation for the value of an American option using a confined exponential distribution with tight upper bounds. This is an extension of the Geske and Johnson compound option approach and the Ho et al. exponential extrapolation method. Use of a perpetual American put value, and then a European put with high input volatility is suggested in order to provide a tighter upper bound for an American put price than simply the exercise price. Numerical results show that the new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also further improves pricing accuracy for short-term options, which may substitute adequately for numerical solutions. As an extension, an analytic approximation is presented for a two-factor American call option.     

Two-dimensional risk-neutral valuation relationships for the pricing of options

The Black–Scholes model is based on a one-parameter pricing kernel with constant elasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel with at least two parameters. We price European-style options on assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met, a two-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationship between the price of the option and the prices of the underlying asset and one other option on the asset is the same as it would be under risk neutrality. In this class of models, the price of the underlying asset and that of one other option take the place of the unknown parameters.      

Building a culture of personal benefits responsibility

Successfully having employees take personal responsibility for their benefits plans requires going beyond the rapid rollout of new benefit plan designs; it requires employers to invest in understanding the complexity of their workforce. This article reviews the evolution of benefit plans and what has arisen as the current state of employee benefits. It then discusses steps employers can take to build a successful total benefit strategy that recognizes the importance of the emerging workforce's racial, ethnic and cultural diversity.     

A subjective assessment of approximate probabilities with a portfolio application

This paper extends the assessment of approximate probabilities in two important directions. The first is to investigate some mathematical relations between the probability ranges and derives the most unbiased probability for the case when the limits are subjectively defined. The second is to suggest a simple method to determine the optimal solution which represents the optimal portfolio proportions of securities that possess the minimum risk measured by the maximum entropy measure. The paper considers the derivation of portfolio modeling under a fuzzy situation using probability theory, and provides various other (non-probabilistic) scenarios with their utility in risk modeling. A simple method for identification of mean-entropic frontier is proposed. Then, a comparison of mean-variance procedure with the discrete mean-entropic method is implemented by an example.     

Retiree health care benefits: strategies for a changing workforce.

Demographic, economic and cultural trends foretell a dramatically different environment for retiree health care coverage. This article will focus on the redesign of retiree health benefits to meet the retirement objectives of employers and employees, anticipate changing demographics, and respond to changes in Medicare and other government initiatives, including the Consumer Bill of Rights. The material will discuss recent design trends, including managed care, and present results of a study the author co-authored for the Kaiser Family Foundation on changes in retiree health plans.     

Portfolio diversification benefits within Europe: Implications for a US investor

This paper investigates the possibility of cointegration between the United States and 11 European equity markets before and after the convergence period of 1995. The results indicate that during the preconvergence and postconvergence periods, some country groups, with and without the US equity market, exhibited cointegration while others did not. For the European Union markets, however, at least one cointegrating vector emerged in either period, but no cointegration among them surfaced during the Euro introduction period of 1999. These results suggest that a US investor can still benefit from country diversification within the European Union markets.     

A model for valuation of the branch offices of a savings bank based on rough sets

This work proposes a model for the valuation of branch of?ces of banks based on the rough set theory, which could be used as the basis for a decision‐making system for dimensioning strategies of a ?nancial entity. It compares the rough set approach with the competitive discriminant analysis methodology using a common set of data from 421 branches. We pay special attention to data reduction and the creation of decision rules that will allow future branches to be classi?ed. These rules could constitute the basis for the evaluation of the viability of dimensioning strategies for a ?nancial entity. In order to evaluate the predictive capabilities of the decision rules, we present the results of cross‐validation tests to evaluate the ability of the model to classify new branches. It appears that the rough sets approach provides a favourable tool for the valuation of branch of?ces. Copyright © 2004 John Wiley & Sons, Ltd.     

Forecasting disability: application of a frailty model

Random changes in individual frailty occur due to the stochastic processes of physical deterioration or environmental influences. This paper implements a stochastic ageing model using maximum likelihood methods and calibrates the model to more than 30 years of historical Australian mortality data in order to examine cohort and gender differences in health-state distributions among older adults. We find that frailty levels have declined over time for both male and female cohorts. Nonetheless, patterns of frailty are different between genders. Older females experience a faster pace of health deterioration than their male counterparts causing them to move quicker into worse states of health. Health states are also more heterogeneous among women than men. Population-level estimates suggest that the number of elderly Australians requiring aged care services will exceed that projected under governmental assumptions by 2050.