OPTIMAL STOPPING OF A RISK RESERVE PROCESS WITH INTEREST AND COST RATES

The risk reserve process of an insurance company within a deterioratin g Markov-modulated environment is considered. The company invests its capital with interest rate alpha; the premiums and claims are increasi ng with rates beta and gamma. The problem of stopping the process at a random time which maximizes the expected net gain in order to calcula te new premiums is investigated. A semimartingale representation of th e risk reserve process yields, under certain conditions, an explicit s olution of the problem.