Michael Sherris

Risk sensitive asset allocation

Abstract This paper develops a continuous time modeling approach for making optimal asset allocation decisions. Macroeconomic and financial factors are explicitly modeled as Gaussian stochastic processes which directly affect the mean returns of the assets. We employ methods of risk sensitive control theory, thereby using an infinite horizon objective that is natural and features the long run expected growth rate and the asymptotic variance as two measures of performance, analogous to the mean return and variance, respectively, in the single period Markowitz model. The optimal strategy is a simple function of the factor levels, and, even with constraints on the portfolio proportions, it can be computed by solving a quadratic program. Explicit formulas can be obtained, as is illustrated by an example where the only factor is a Vasicek-type interest rate and where there are two assets: cash and a stock index. The methods are further illustrated by studies of two data sets: U.S. data with two assets and up to three factors, and Australian data with three assets and three factors.

The Valuation of Option Features in Retirement Benefits

This article extends and applies a contingent claims valuation approach to option features in retirement fund benefits. The approach incorporates retirement, mortality, and other decrements and allows for differences between the benefit payments and standard option payoffs. A discrete lattice implementation commonly used for valuing financial options is found to be unsatisfactory for the valuation of these option features. Simulation is found to be more efficient. Simulation is then used to calculate benefit values for a range of ages for a simplified fund. The results of the valuations for a number of simulation scenarios demonstrate that a traditional deterministic actuarial valuation can understate the cost of these benefits by as much as 25 to 35 percent.

The Determinants of External Audit Costs in the New Zealand Life Insurance Industry

The contracting theory literature suggests that auditors’ pricing decisions reflect the efficacy of contracting arrangements in firms. Drawing a framework from this literature, we test empirically the simultaneous effect of six firm-specific variables on external audit costs using 1988–1993 data drawn from New Zealand’s (NZ) life insurance industry. These variables are: assets-in-place, reinsurance, internal governance, firm size, product-mix and organizational form. Consistent with expectations, our results indicate that audit fees are influenced by product-mix and firm size. However, the other variables are found not to be statistically significant. The empirical results thus provide mixed support for contracting theory.

Risk measures and insurance premium principles

Abstract Risk measures based on distorted probabilities have been recently developed in actuarial science and applied to insurance rate making. We propose a risk measure that has the properties of risk aversion and diversification, is additive for losses and consistent in its treatment of insurance and investment risks. We show that the risk measure based on distorted probabilities is not consistent in its ordering of insurance and investment risks.

Simulating from Exchangeable Archimedean Copulas

Multivariate exchangeable Archimedean copulas are one of the most popular classes of copulas that are used in actuarial science and finance for modeling risk dependencies and for using them to quantify the magnitude of tail dependence. Owing to the increase in popularity of copulas to measure dependent risks, generating from multivariate copulas has become a very crucial exercise. Current methods for generating from multivariate Archimedean copulas could become a very difficult task as the number of dimension increases. The resulting analytical procedures suggested in the existing literature do not offer much guidance for practical implementation. This article presents an algorithm for generating values from the multivariate exchangeable Archimedean copulas based on a multivariate extension of a bivariate result. A procedure for generating values from bivariate Archimedean copulas has been originally proposed in Genest and Rivest (1993) and again later described in Nelsen (1999) and Embrechts et al. (2001a b). Using a proof that is simply based on fundamental Jacobian techniques for deriving distributions of transformed random variables, we are able to extend the bivariate result into the multivariate case allowing us to develop an interesting algorithm to generate values from exchangeable Archimedean copulas. As auxiliary results, we are able to derive the distribution function of an n-dimensional Archimedean copula, a result already known in Genest and Rivest (2001), but our approach of proving this result is based on a different perspective. This article focuses on this class of copulas that has one generating function and one parameter that characterizes the dependence structure of the joint distribution function.

Enterprise Risk Management, Insurer Value Maximisation, and Market Frictions

Enterprise risk management has become a major focus for insurers and reinsurers. Capitalization and pricing decisions are recognized as critical to …rm value maximization. Market imperfections including frictional costs of capital such as taxes, agency costs, and …nancial distress costs are an important motivation for enterprise risk management. Risk management reduces the volatility of …nancial performance and can have a signi…cant impact on …rm value maximization by reducing the impact of frictional costs. Insurers operate in imperfect markets where demand elasticity of policyholders and preferences for …nancial quality of insurers are important determinants of capitalization and pricing strategies. In this paper, we analyze the optimization of enterprise or …rm value in a model with market imperfections. A realistic model of an insurer is developed and calibrated. Frictional costs, imperfectly competitive demand elasticity, and preferences for …nancial quality are explicitly modelled and implications for enterprise risk management are quanti…ed. �Acknowledgement: The authors acknowledge …nancial support from Australian Research Council Discovery Grants DP0663090 and DP0556775 and support from the UNSW Actuarial Foundation of the Institute of Actuaries of Australia. Yow acknowledges the …nancial support of Ernst and Young and the award of the Faculty of Business Honours Year Scholarship.

Systematic Mortality Risk: An Analysis of Guaranteed Lifetime Withdrawal Benefits in Variable Annuities

Guaranteed lifetime withdrawal benefits (GLWB) embedded in variable annuities have become an increasingly popular type of life annuity designed to cover systematic mortality risk while providing protection to policyholders from downside investment risk. This paper provides an extensive study of how different sets of financial and demographic parameters affect the fair guaranteed fee charged for a GLWB as well as the profit and loss distribution, using tractable equity and stochastic mortality models in a continuous time framework. We demonstrate the significance of parameter risk, model risk, as well as the systematic mortality risk component underlying the guarantee. We quantify how different levels of equity exposure chosen by the policyholder affect the exposure of the guarantee providers to systematic mortality risk. Finally, the effectiveness of a static hedge of systematic mortality risk is examined allowing for different levels of equity exposure.

Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory

This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.

Managing Systematic Mortality Risk with Group Self‐Pooling and Annuitization Schemes

Group Self-annuitisation Schemes (GSAs), or Pooled Annuity Schemes, are designed to share uncertain future mortality experience including systematic improvements. They have been proposed because of the significant uncertainty of future mortality improvement on pension and annuity costs. The challenges for designing group pooled schemes include the decreasing average payments when mortality improves significantly, the decreasing numbers in the pool at the older ages and the dependence of systematic mortality improvements across different ages of members in the pool.

Heterogeneity of Australian Population Mortality and Implications for a Viable Life Annuity Market

Heterogeneity in mortality rates is known to exist in populations, undermining the use of age and sex as the only rating factors for life insurance and annuity products. Life insurers offering life annuities assume that annuitant lives will self-select, and price the longevity risk with an annuity mortality table that assumes above-average longevity. This leads to annuities being less attractive to a wide range of individuals, and limits the viability of private annuity markets. This paper quantifies heterogeneity and its financial implications for annuity prices using well-established frailty models and a more recently developed Markov ageing model calibrated to population mortality data. The heterogeneity implied for each model is quantified using Australian population mortality. The models are compared by considering the distribution of heterogeneity by age implied by the models and the implications for life annuity prices.