Abstract: In this talk, we study a risk-sensitive portfolio optimization problem with a finite time horizon in a financial market consisting of one risk-free asset and one risky asset. The price dynamics of the risky asset are governed by an α-hypergeometric stochastic volatility model, where the volatility factor follows a positive solution of a linear stochastic differential equation. Using a dynamic programming approach, we derive the associated Hamilton--Jacobi--Bellman (HJB) equation. Furthermore, by applying a suitable Feynman--Kac representation, we establish the existence and uniqueness of a classical solution for the HJB equation. Finally, we prove a verification theorem and construct the optimal investment strategy. 

 

Organizer: Shang-Yuan Shiu (NCU)