Constrained Investment and Reinsurance with Ambiguous Correlations

This paper explores the optimal investment and reinsurance problem with the objective of maximizing the probability of reaching a bequest goal, while accounting for constraints and ambiguous correlations. Specifically, the study considers two types of constraints: no short-selling constraints and constant barrier constraints. Ambiguous correlation refers to a scenario where the correlation coefficient between the financial market and the insurance market falls within a certain interval, and where there is no clear probability distribution for the value. Using the dynamic programming principle, this study derives the HJB equation associated with the optimal control problem and provides explicit expressions for the value function and optimal strategies through the application of the “ellipse maximization” method