| Title |
The analysis of the Gerber-Shiu discounted penalty function / |
| Translation of Title |
Gerber-Shiu diskontuotos baudos funkcijos tyrimas. |
| Authors |
Kočetova, Jelena |
| Full Text |
|
| Pages |
16 |
| Keywords [eng] |
Gerber-Shiu discounted penalty function ; renewal risk model ; renewal process ; renewal equation |
| Abstract [eng] |
The Gerber-Shiu discounted penalty function was the main object of investigations in the thesis. This function is very effective tool in modelling activity of insurance company, because it describes the expectation of the present value of a future bankruptcy. An insurer may evaluate company's safety level and manage the risk by taking into consideration the values of mentioned function. In the dissertation the explicit expressions of this function was got in the classical risk model by using appropriate distributions of the claim amount. Applying these expressions the dependence of the discounted penalty function on initial capital, interest rate, safety loading and claim intensity was studied. The asymptotics of the discounted penalty function in the Erlang(2) model with subexponential claims was also considered in the thesis. The asymptotic formula for this function was derived. The formula has a simple form what facilitates analysis of the discounted penalty function when initial capital becomes extremely large. The renewal counting process was also studied in the thesis. Generally this process widely applied with different risk models where represents the number of claims up to some time point. Some properties of this process was investigated in the thesis and asymptotics of the tail of the exponential moment was derived. The obtained result was applied to the asymptotic’s analysis of the finite time ruin probability in a renewal risk model. |
| Type |
Summaries of doctoral thesis |
| Language |
English |
| Publication date |
2011 |
