In this talk, we begin with a risk-sensitive portfolio optimization problem formulated under a stochastic factor model, and introduce its mathematical structure and analytical approach based on dynamic programming, particularly the Hamilton-Jacobi-Bellman (HJB) equation. We then explore the duality between risk-sensitive evaluation and large deviations control, and discuss problem formulations from the perspective of long-term asset management—namely, maximizing growth opportunities and minimizing downside risks.
In the latter part, we address limitations of conventional affine-type models and introduce the α-Hypergeometric stochastic volatility model, which allows for more flexible and realistic volatility dynamics. We report on the analysis of the risk-sensitive portfolio optimization problem under this model, including the derivation of nonlinear partial differential equations, their probabilistic representations, the construction of optimal strategies, and the verification theorem. Through these developments, we demonstrate a concrete application of stochastic control theory within the framework of mathematical finance.

16:15 - Tea