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 α-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.
- Feynman-Kac representation
- Hamilton-Jacobi-Bellman equation
- Portfolio problem
- Stochastic volatility
- Utility function