| Abstract [eng] |
In the financial management of insurance companies and other financial systems an important aspect are dividends. Consider the situation dividends are paid to the shareholders of the insurance company according to barrier strategy with parameter b. In practical situations complete information about the individual claim amount distribution is often not known and the company faces the difficulty in finding the optimal dividend barrier. Model of an insurance company is defined in such way: the premiums of a company are received at rate c, the agregate claims process {S(t)} is a compound Poisson process with Poisson parameter λ and the probability density function of an individual claim amount is denoted by p(y), y>0. In the following, the moment of an individual claim amount distribution of order k will be denoted as pk, k=1, 2, 3,.... Often when complete information about the individual claim amount distribution is not known, estimates for the first few moments of this distribution are available. For such a situation, in this paper methods for estimating the optimal dividend barrier are examined. De Vylder A approximation requires knowledge of p1, p2 and p3. De Vylder B requires knowledge of p1 and p2. Wiener approximation requires knowledge of the same information as De Vylder B, while the diffusion approximation of order k requires knowledge of p1, p2, …, pk+2 . In order to illustrate the approximation methods for several claim amount distributions De Vylder A, De Vylder B, Wiener, I order and II order approximations are applied. The approximate values are compared with the exact values. From the obtained results we can note, that approximations which use third moment of the claim amount distribution are more accurate than that which use second moment. The diffusion approximation of order 2 also uses the fourth moment. In some cases it provides better results than De Vylder A and always better results than diffusion approximation of order 1. |
