Optimal Insurance Indemnity and Reinsurance Strategy for Health Insurance

"Health insurance + health management" package has recently become one of the most important nonlife insurance products, and its pricing technique has drawn attention from both academia and industry. This paper investigates the optimal indemnity design and per-loss reinsurance strategy for the health insurance package, where the reinsurance contract is assumed to combine the quota-share type and the excess-of-loss type. By applying the Lagrange multiplier method and optimal control technique, we develop the solutions to the corresponding optimization problems and obtain the optimal deductible. Then, we proceed to solve the optimal quota-share proportion and the optimal stop-loss retention based on the optimal insurance indemnity. In addition to theoretical results, numerical examples are also given to illustrate the effects of various key parameters on the optimal indemnity design and combinational reinsurance strategy.