A Discrete Time Benchmark Approach for Insurance and Finance

Hans Bühlmann · Eckhard Platen

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

Abstract

This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as reference unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales. Benchmarked fair price processes are characterized as martingales. No measure transformation is needed for the fair pricing of insurance policies and derivatives. The standard actuarial pricing rule is obtained as a particular case of fair pricing when the contingent claim is independent from the growth optimal portfolio. 1991 Mathematics Subject Classification: primary 90A12 secondary 60G30, 62P20 JEL Classification: G10, G13

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1993Dynamic Asset Pricing Theory.1998Methods of Mathematical Finance 1999The asymptotic elasticity of utility functions and optimal investment in incomplete markets 1998Methods of Mathematical Finance 1992A Theory of the Nominal Term Structure of Interest Rates 1998Mathematics of Derivative Securities 1990The numeraire portfolio 1997The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates

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