The influence of bankruptcy value on optimal risk control for diffusion models with proportional reinsurance

This paper considers the model of a financial entity such as an insurance company whose surplus is governed by a Brownian motion with constant drift and diffusion coefficient. A proportional reinsurance available to the company allows it to reduce its risk by simultaneously reducing the diffusion coefficient and the drift. The uncontrolled dividends are accumulated at the rate proportional to the current value of the surplus. It is assume that at the time of bankruptcy the company liquidation (bankruptcy or terminal) value is P. The objective is to find the policy which maximizes the total discounted value of dividends and the terminal value of the company. We find the optimal policy and analyze its dependence on P.