Optimal Portfolio for the $\alpha$-Hypergeometric Stochastic Volatility Model

Source abstract

In this article we study an optimal portfolio problem for an investor with constant relative risk aversion that trades in a market with asset prices described by the $\alpha$-hypergeometric stochastic volatility model. To determine the optimal strategy, we follow the dynamic programing approach. Namely, using a suitable Feynman--Kac representation, we construct a classical solution for the corresponding Hamilton--Jacobi--Bellman equation. In order to verify that the solution of the Hamilton--Jacobi--Bellman equation coincides with the value function, we establish a verification theorem. In addition, we present several numerical simulations based on the proposed Feynman--Kac representation.