Aproksymacje prawdopodobieństwa ruiny firmy ubezpieczeniowej w dyfuzyjnym modelu Coxa - Palmowski, Zbigniew (Approximations of the Ruin Probability of an Insurance Company in a Diffusion Cox Model, 2006)
Schmock suggested a random intensity of arrivals of claims in the portfolio of the vehicle insurance policies of the Winterhur insurance company in Switzerland. This variability may be explained by a random number of policies in a portfolio, increasing market share, change of habits of the clients, dependence on the season and so on. To catch these changes in the intensity of the arrival process of the claims we analyze diffusion type of variability. In the paper we construct diffusion Cox model describing the risk reserve process of an insurance company. In this model we prove Lundberg inequalities and approximations of the ruin probability. Ruin probability describes the chance that reserves of an insurance company become negative and it is a basis for calculating the risk of the insurer. It is then one of the most basic quantities in the insurance theory. In this paper we will explain the difference of the fluctuations of the reserves of an insurance company in the case of small, classic arriving claims and huge claims coming from storms, earthquakes, terrorist attacks etc. Mathematical methods are based on the martingale techniques and the theory of heavy-tailed random walks introduced in author's papers.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2006; nr 1108, s. 34-54