Stochastic Perron's Method for the Probability of Lifetime Ruin Problem Under Transaction Costs
SIAM Journal on Control and Optimization, 53(1), 91-113, 2015
24 Pages Posted: 30 Apr 2014 Last revised: 9 May 2015
Date Written: April 29, 2014
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.
Keywords: Stochastic Perron's method, singular control, probability of lifetime ruin, transaction costs, viscosity solutions, comparison principle
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