Modeling of an insurance system and its large deviations analysis

✍ Scribed by Ali Devin Sezer

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 510 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.06.003

✦ Synopsis

We model an insurance system consisting of one insurance company and one reinsurance company as a stochastic process in R 2 . The claim sizes {X i } are an iid sequence with light tails. The interarrival times {τ i } between claims are also iid and exponentially distributed. There is a fixed premium rate c 1 that the customers pay; c < c 1 of this rate goes to the reinsurance company. If a claim size is greater than R the reinsurance company pays for the claim. We study the bankruptcy of this system before it is able to handle N number of claims. It is assumed that each company has initial reserves that grow linearly in N and that the reinsurance company has a larger reserve than the insurance company. If c and c 1 are chosen appropriately, the probability of bankruptcy decays exponentially in N. We use large deviations (LD) analysis to compute the exponential decay rate and approximate the bankruptcy probability. We find that the LD analysis of the system decouples: the LD decay rate γ of the system is the minimum of the LD decay rates of the companies when they are considered independently and separately. An analytical and numerical study of γ as a function of (c, R) is carried out.