Deep Learning Solution of Optimal Reinsurance-Investment Strategies with Inside Information and Multiple Risks

This paper investigates an optimal investment-reinsurance problem for an insurer who possesses inside information regarding the future realizations of the claim process and risky asset process. The insurer sells insurance contracts, has access to proportional reinsurance business, and invests in a financial market consisting of three assets: one risk-free asset, one bond, and one stock. Here, the nominal interest rate is characterized by the Vasicek model, and the stock price is driven by Heston's stochastic volatility model. Applying the enlargement of filtration techniques, we establish the optimal control problem in which an insurer maximizes the expected power utility of the terminal wealth. By using the dynamic programming principle, the problem can be changed to four-dimensional Hamilton-Jacobi-Bellman equation. In addition, we adopt a deep neural network method by which the partial differential equation is converted to two backward stochastic differential equations and solved by a stochastic gradient descent-type optimization procedure. Numerical results obtained using TensorFlow in Python and the economic behavior of the approximate optimal strategy and the approximate optimal utility of the insurer are analyzed.