Stochastic Perron's Method for the Probability of lifetime ruin problem under transaction costs

Erhan Bayraktar and Yuchong Zhang

Papers from arXiv.org

Abstract: We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on the dynamic programming principle (DPP), we characterize the value function as the unique viscosity solution of an associated Hamilton-Jacobi-Bellman (HJB) variational inequality. We also provide a complete proof of the comparison principle which is the main assumption of stochastic Perron's method.

Date: 2014-04, Revised 2014-11
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