Stochastic volatility asymptotics for optimal subsistence consumption and investment with bankruptcy

Optimal subsistence consumption and investment problem with bankruptcy is a constrained stochastic optimal control problem in which the consumption rate should be greater than a non-negative subsistence level to maintain a... [ view full abstract ]

Optimal subsistence consumption and investment problem with bankruptcy is a constrained stochastic optimal control problem in which the consumption rate should be greater than a non-negative subsistence level to maintain a minimal living standard and the wealth level stays positive. When the agent invests in a risky asset which has multiscale stochastic volatility, we extend the framework of Fouque et al. (Portfolio optimization & stochastic volatility asymptotics, Mathematical Finance 27(3), 704-745, 2017) to derived closed-form first-order asymptotic approximation to the optimal consumption-investment strategy and the value function. The major difficulty stems on the subsistence constraint.