Stochastic Volatility Asymptotics for Optimal Subsistence Consumption and Investment with Bankruptcy
23 Pages Posted: 11 Oct 2018 Last revised: 17 Oct 2018
Date Written: September 16, 2018
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.
Keywords: optimal investment and consumption, subsistence consumption, stochastic volatility, asymptotic optimality, perturbation
JEL Classification: C61, G11
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