Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion
We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky asset. Using stochastic control, we characterize the value function as the unique classical solution of an associated Hamilton-Jacobi-Bellman (HJB) equation, obtain feedback forms for the optimal investment and drift distortion, and discuss their dependence on various model parameters. In analyzing the HJB equation, we establish the existence and uniqueness of viscosity solution using Perron's method, and then upgrade regularity by working with an equivalent convex problem obtained via the Cole-Hopf transformation. We show the original value function may lose convexity for a class of parameters and the Isaacs condition may fail. Numerical examples are also included to illustrate our results.
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- Erhan Bayraktar & Virginia Young, 2007.
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- Erhan Bayraktar & Virginia R. Young, 2007. "Minimizing the Probability of Lifetime Ruin under Borrowing Constraints," Papers math/0703850, arXiv.org.
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"Minimizing the Probability of Lifetime Ruin under Stochastic Volatility,"
1003.4216, arXiv.org, revised May 2011.
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"Proving regularity of the minimal probability of ruin via a game of stopping and control,"
Finance and Stochastics,
Springer, vol. 15(4), pages 785-818, December.
- Erhan Bayraktar & Virginia R. Young, 2007. "Proving Regularity of the Minimal Probability of Ruin via a Game of Stopping and Control," Papers 0704.2244, arXiv.org, revised Aug 2010.
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