Articlegreen2007

Stochastic Life Annuities

36 citations0/0 files storedNorth American Actuarial Journal

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Stochastic processes and financial applications Insurance, Mortality, Demography, Risk Management Probability and Risk Models

Abstract

This paper gives analytic approximations for the distribution of a stochastic life annuity. It is assumed that returns follow a geometric Brownian motion. The distribution of the stochastic annuity may be used to answer questions such as “What is the probability that an amount F is sufficient to fund a pension with annual amount y to a pensioner aged x?” The main idea is to approximate the future lifetime distribution with a combination of exponentials, and then apply a known formula (due to Marc Yor) related to the integral of geometric Brownian motion. The approximations are very accurate in the cases studied.

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References

1973The Pricing of Options and Corporate Liabilities 1981Martingales and stochastic integrals in the theory of continuous trading 1900Théorie de la spéculation 1959Brownian Motion in the Stock Market 1986Actuarial Mathematics.1993BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES 1990The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding 2001Exponential Functionals of Brownian Motion and Related Processes

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