Title: Optimal risk control with both fixed and proprotional transaction costs
Authors: Ming Zhou - Central University of Finance and Economics (China) [presenting]
KC Yuen - HKU (China)
Abstract: A large insurance company is considered whose cumulative cash flow process is described by a drifted Brownian motion. The decision maker of the company has an option to purchase proportional reinsurance at a point of time to minimize the ruin probability and maximize the expected present value of dividend payments up to the time of ruin. In view of the expenses like consultant commission in practice, it is assumed that a fixed transaction cost occurs at the beginning of a reinsurance treaty, and that the reinsurance is irreversible. For this mixed problem of optimal stopping time and stochastic control, we are able to derive the optimal time to purchase the reinsurance, the optimal retained proportion, the optimal dividend barrier, and the value function. The optimal solution shows that reinsurance is valueless to the firm value when the fixed cost is large, and comes into play when the fixed cost is moderate. We also carry out some numerical studies to assess the impact of the fixed cost on the value function and the optimal policies.