| Title |
Bankroto tikimybė nehomogeniniam rizikos atstatymo modeliu / |
| Translation of Title |
Ruin probability for inhomogeneous renewal risk model. |
| Authors |
Bernackaitė, Emilija |
| Full Text |
|
| Pages |
23 |
| Keywords [eng] |
Inhomogeneous renewal risk model ; Ruin probability ; Lundberg-type inequality ; Renewal process |
| Abstract [eng] |
In the thesis ruin probability in an inhomogeneous renewal risk model is investigated. The main purpose of the thesis is to find conditions such that we could apply similar estimations of ruin probability for an inhomogeneous renewal risk model like for the homogeneous one. A Lundberg-type inequality is obtained in the case of an inhomogeneous renewal risk model. We consider the model with independent, but not necessarily identically distributed, claim sizes and the inter-occurrence times. The asymptotic behaviour of the exponential moment tail of inhomogeneous renewal process is considered and it is proved that this moment tail vanishes at infinity. This property holds for inter-arrival times having different distributions and satisfying certain dependence structures. The obtained property is used to prove the weak law of large numbers for an inhomogeneous renewal process. Additional corollaries are presented concerning elementary renewal theorems for the inhomogeneius renewal process. Finally, an asymptotic formula is given for the finite-time ruin probability in an inhomogeneous renewal risk model. We consider the renewal risk model with independent strongly subexponential claim sizes and independent not necessarily identically distributed inter-occurrence times having finite variances. We find out that the asymptotic formula for the finite-time ruin probability is insensitive to the homogeneity of inter-occurrence times. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Summaries of doctoral thesis |
| Language |
Lithuanian |
| Publication date |
2016 |
