Abstracts

This paper concerns the the optimal asset allocation of an investor in the presence of stochastic interest rates and a nonnegative stochastic mortality rate. A complete market setting is assumed where wealth can be invested in a zero-coupon bond, a survival bond, a stock and the money-market account. Survival bonds, which pay the difference between realized and expected mortality for a given population, can be thought of as an insurance against changes in survival probabilities. The investor, whose lifetime is uncertain, derives utility from accumulated wealth at his/her retirement date and utility from intermediate consumption. The mortality of the agent is modelled by a doubly stochastic Poisson process; the mortality rate and the short rate are assumed to follow independent Cox-Ingersoll-Ross processes. Using dual methods it will be shown that this problem has a closed-form solution. Conditions for existence of an optimal solution will be provided in terms of the model parameters. To derive these, we extend results by [1], [2] and [3]. We use a result by [4] to establish finiteness of the value function.

[1] G. Deelstra, M. Grasselli and P.F. Koehl (2000). Optimal investment strategies in a CIR framework. J. Appl. Prob. 37, 936-946.
[2] H. Kraft (2003). Optimal portfolios with stochastic interest rates and defaultable assets. Springer.
[3] H. Kraft (2009). Optimal portfolios with stochastic short rate: Pitfalls when the short rate is non-Gaussian or the market price of risk is unbounded. J. of Theoretical and Applied Finance 12, 767-796.
[4] T.R. Hurd and A. Kuznetsov (2008). Explicit formulas for Laplace transforms of stochastic integrals. Markov Processes and Related Fields 14, 277--290.