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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

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yuchong Zhang

Columbia University

Date Written: April 29, 2014

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.

Keywords: Stochastic Perron's method, singular control, probability of lifetime ruin, transaction costs, viscosity solutions, comparison principle

Suggested Citation

Bayraktar, Erhan and Zhang, Yuchong, Stochastic Perron's Method for the Probability of Lifetime Ruin Problem Under Transaction Costs (April 29, 2014). SIAM Journal on Control and Optimization, 53(1), 91-113, 2015. Available at SSRN: https://ssrn.com/abstract=2430858 or http://dx.doi.org/10.2139/ssrn.2430858

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yuchong Zhang

Columbia University ( email )

1255 Amsterdam Avenue
New York, NY 10027
United States

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