SOME ADVANCES ON THE ERLANG(n) DUAL RISK MODEL
| Autor: | Rui M.R. Cardoso, Alfredo D. Egídio dos Reis, Eugenio V. Rodríguez-Martínez |
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| Rok vydání: | 2014 |
| Předmět: |
Economics and Econometrics
Exponential distribution Laplace transform Dual model Generalized Lundberg’s Equation Time of Ruin Ruin Probability Erlang (unit) Risk model Constant rate Expected Discounted Dividends Accounting Dividend Applied mathematics Phase-type distribution Operations management Phase–Type Distribution Dual Risk Model Erlang(n) Interarrival Times Finance Mathematics |
| Zdroj: | ASTIN Bulletin. 45:127-150 |
| ISSN: | 1783-1350 0515-0361 |
| DOI: | 10.1017/asb.2014.19 |
| Popis: | The dual risk model assumes that the surplus of a company decreases at a constant rate over time and grows by means of upward jumps, which occur at random times and sizes. It is said to have applications to companies with economical activities involved in research and development. This model is dual to the well-known Cramér-Lundberg risk model with applications to insurance. Most existing results on the study of the dual model assume that the random waiting times between consecutive gains follow an exponential distribution, as in the classical Cramér-Lundberg risk model. We generalize to other compound renewal risk models where such waiting times are Erlang(n) distributed. Using the roots of the fundamental and the generalized Lundberg's equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Furthermore, we compute expected discounted dividends, as well as higher moments, when the individual common gains follow a Phase-Type, PH(m), distribution. We also perform illustrations working some examples for some particular gain distributions and obtain numerical results. |
| Databáze: | OpenAIRE |
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