Minimizing the Probability of Lifetime Ruin under Random Consumption

North American Actuarial Journal
Volume 12, Issue 4, 2008
Erhan Bayraktar PhD, Kristen S. Moore PhD, ASA & Virginia R. Young PhD, FSA

Abstract

We determine the optimal investment strategy in a financial market for an individual whose random consumption is correlated with the price of a risky asset. Bayraktar and Young consider this problem and show that the minimum probability of lifetime ruin is the unique convex, smooth solution of its corresponding Hamilton-Jacobi-Bellman equation. In this paper we focus on determining the probability of lifetime ruin and the corresponding optimal investment strategy. We obtain approximations for the probability of lifetime ruin for small values of certain parameters and demonstrate numerically that they are reasonable ones. We also obtain numerical results in cases for which those parameters are not small.

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