Tweedie 분포 하에서 Stop-Loss 재보험 의 가치측정

When loss distribution of insurance follows compound Poisson process, intensity of loss can be generally supposed in constant but the severity can be postulated to gamma distribution, exponential distribution etc. At this time, distribution function about the stochastic process can be derived under very limited assumption about the severity. When loss function follows this compound Poisson process, Smyth-Jorgensen(2002) provide empirical evidence for fair insurance premium. In the mean time, Jang-Wong(2003) suggests pricing model of excess-loss reinsurance that measures the value of tariffs using Esscher transform method. However, Jang-Wong(2003) has problem that choose parameter voluntarily because their model numerically measure the tariffs without presenting the relation between empirics and pricing model. Reinsurance can be priced by directly estimating compound Poisson distribution function, or by simulating method. In the case of these methods, the value of reinsurance is determined by using the factor loading that issuer`s utility function is reflected. However, Esscher transform method with property of martingale has advantage that can effectively reflect opportunity cost in capital market. Therefore, We derive value(i.e. pure premium) formula of Stop-Loss reinsurance by Esscher transformation which reflects compensated compound Poisson process to the price of original insurance.