Stochastic Volatility Asymptotics for Optimal Subsistence Consumption and Investment with Bankruptcy

Abstract

Subsistence consumption and investment problems with bankruptcy are classic constrained stochastic optimal control problem in financial economic, where the consumption rate should be greater than a positive number and the investor faces a bankruptcy payment. We derive novel asymptotic solution to this problem under the fast mean-reverting stochastic volatility model. We rigorously prove that the zeroth-order approximation for the optimal pair of consumption and investment strategies leads to the first-order accuracy of the objective function. In addition, this zeroth-order suboptimal consumption-investment pair is asymptotically optimal in a class of admissible trading strategy pairs.