| Title |
Martingale approach to derive Lundberg-type inequalities / |
| Authors |
Kuras, Tautvydas ; Sprindys, Jonas ; Šiaulys, Jonas |
| DOI |
10.3390/math8101742 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2020, vol. 8, iss. 10, art. no. 1742, p. 1-18.. ISSN 2227-7390 |
| Keywords [eng] |
exponential estimate ; supremum of sums ; tail probability ; risk model ; inhomogeneity ; ruin probability ; Lundberg's inequality |
| Abstract [eng] |
In this paper, we find the upper bound for the tail probability P(supn⩾0∑ni=1ξi>x) with random summands ξ1,ξ2,… having light-tailed distributions. We find conditions under which the tail probability of supremum of sums can be estimated by quantity ϱ1exp{−ϱ2x} with some positive constants ϱ1 and ϱ2. For the proof we use the martingale approach together with the fundamental Wald’s identity. As the application we derive a few Lundberg-type inequalities for the ultimate ruin probability of the inhomogeneous renewal risk model. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2020 |
| CC license |
|
