Muciek, Bogdan Krzysztof (2003), Optimal stopping of a risk process with interest rates, Computing Science and Statistics, 35, I2003Proceedings/MuciekBogdan/MuciekBogdan.paper.pdf ,
Muciek, Bogdan Krzysztof (2003), On optimal stopping of risk reserve process, Computing Science and Statistics, 35, I2003Proceedings/MuciekBogdan/MuciekBogdan.presentation.pdf
The following problem in risk theory is considered. An insurance company, endowed with an initial capital, receives premiums and pays out claims that occur according to a renewal process. The times between consecutive claims are independent and identically distributed (i.i.d.). The sequence of successive claims is a sequence of i.i.d. random variables. The capital of the company is invested with an interest rate, claims increase with another rate. The aim is to find the stopping time that maximizes the capital of the company. A dynamic programming method is used to find the optimal stopping time and to specify the expected capital at that time. The cases of immidiate claim payout as well as at the end of periods are considered.