Loading...
Please wait, while we are loading the content...
Similar Documents
Approximations for the Gerber-Shiu expected discounted penalty function in the compound poisson risk model
| Content Provider | Scilit |
|---|---|
| Author | Pitts, Susan M. Politis, Konstadinos |
| Copyright Year | 2007 |
| Description | In the classical risk model with initial capital u, let τ(u) be the time of ruin, X$ _{+}$(u) be the risk reserve just before ruin, and Y$ _{+}$(u) be the deficit at ruin. Gerber and Shiu (1998) defined the function m$ _{δ}$(u) $=E[e^{−δ τ(u)}$ w(X$ _{+}$(u), Y$ _{+}$(u)) 1 (τ(u) < ∞)], where δ ≥ 0 can be interpreted as a force of interest and w(r,s) as a penalty function, meaning that m$ _{δ}$(u) is the expected discounted penalty payable at ruin. This function is known to satisfy a defective renewal equation, but easy explicit formulae for m$ _{δ}$(u) are only available for certain special cases for the claim size distribution. Approximations thus arise by approximating the desired m$ _{δ}$(u) by that associated with one of these special cases. In this paper a functional approach is taken, giving rise to first-order correction terms for the above approximations. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/342EFBA2157EBAF5C099F10F4E716EFB/S0001867800001816a.pdf/div-class-title-approximations-for-the-gerber-shiu-expected-discounted-penalty-function-in-the-compound-poisson-risk-model-div.pdf |
| Ending Page | 406 |
| Page Count | 22 |
| Starting Page | 385 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/s0001867800001816 |
| Journal | Advances in Applied Probability |
| Issue Number | 02 |
| Volume Number | 39 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2007-06-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Applied Mathematics Time of Ruin Deficit At Ruin Surplus Prior To Ruin Defective Renewal Equation Functional Approach |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
