Equilibrium investment-reinsurance strategy with delay and common shock dependence under Heston's SV model

This paper investigates an investment and reinsurance problem with delay and common shock dependence under the mean-variance utility framework. We first use Heston's SV model to depict the financial market and two-dimensional Poisson process with common shock dependence to characterize the surplus process. We then introduce the past performance and use it to derive the wealth process depicted by the stochastic delay differential equation. Applying the stochastic control theory within the framework of the game theory, and stochastic control theory with delay, we derive an extended Hamilton-Jacobi-Bellman equation with delay. By solving the equation, we obtain the equilibrium strategy and the corresponding equilibrium value function. We also provide a numerical example to analyze the effects of delay parameters and co-shocks parameters on equilibrium strategy and explain why such effects occur.