Risk-sensitive benchmarked portfolio optimization under non-linear market dynamics

Abstract

We discuss a continuous-time portfolio optimization problem to beat a stochastic benchmark. The model considers non-linear stochastic differential equations (SDEs) to model the dynamics of assets and economic factors. Unlike existing literature on risk-sensitive criteria, the proposed framework allows the model to capture the non-linearity in assets and factors dynamics. This article contributes to the two essential aspects of the problem; first, the existence and uniqueness of optimal investment strategy, which we prove using stochastic control theory and shows optimal strategies remain unchanged for the finite and infinite time horizon problems. Second, we use forecasting to compare investment performance under different economic factors. We analyze returns for the proposed model for three years in two important financial markets; S&P 100 and Dow 30. Risk versus return analysis indicates the importance of choosing relevant economic factors and their model for better portfolio performance. The results suggest an excellent bet to select the non-linear model over the linear one.