Abstract

We consider an optimal consumption and investment problem with delay under a linear Gaussian stochastic factor model. A linear Gaussian stochastic factor model is a stochastic factor model in which the mean returns of risky assets depend linearly on underlying economic factors that are formulated as the solutions of linear stochastic differential equations. We consider the performance-related capital inflow/outflow, which implies that the wealth process is modeled by a stochastic differential delay equation. We also treat the partial information case where the investor cannot observe the factor process and can use only past information about risky assets. Under this setting, the investor tries to maximize the finite horizon discounted expected HARA utility of consumption, the terminal wealth, and the average wealth. A pair of forward-backward stochastic differential equations derived via the stochastic maximum principle have an explicit solution that can be obtained by solving a time-inhomogeneous Riccati differential equation. Thus, the optimal strategy and the optimal value can be obtained explicitly.

 

Organizers: Shang-Yuan Shiu (NCU), Jhih-Huang Li (NTU), Wai Kit Lam (NTU)