Risk-sensitive asset management in a general diffusion factor model: risk-seeking case

Abstract

We consider risk-sensitive asset management on both finite and infinite time horizons. In particular, we treat the risk-seeking case. The returns and volatilities of the assets are random and affected by some economic factors, modeled as a diffusion process. The problems become standard risk-sensitive control problems. We derive the Hamilton–Jacobi–Bellman equations and study these solutions. Using solutions, we construct optimal strategies and optimal values. Moreover, we solve an upside large deviations probability maximization problem by conducting the duality relation with the infinite time horizon problem.