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Stochastic Perron's Method for the Probability of lifetime ruin problem under transaction costs
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.Comment: Final version: To appear in SIAM Journal on Control and Optimization.
Keywords: Stochastic Perron's method, singular control, probability of
lifetime ruin, transaction costs, viscosity solutions, comparison principle.
24 page