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 problems in financial economics, where the consumption rate should be greater than a positive number and the investor faces a bankruptcy payment. We derive a novel asymptotic solution to this problem under the fast mean-reverting stochastic volatility model. We rigorously prove that the zeroth-order suboptimal pair of consumption and investment strategies leads to the first-order correction of the objective function in the form of v(0) + √ϵv(1). In addition, this zerothorder suboptimal consumption-investment pair is asymptotically optimal in a class of admissible trading strategy pairs. © 2019 Society for Industrial and Applied Mathematics.