Ruin probabilities for a Lévy-driven generalised Ornstein-Uhlenbeck process
We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent Levy processes. Our main ´ interest is the model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset...
| Published in: | Finance and stochastics Vol. 24, № 1. P. 39-69 |
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| Format: | Article |
| Language: | English |
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| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000791247 Перейти в каталог НБ ТГУ |
| Summary: | We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent Levy processes. Our main ´ interest is the model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let β > 0 be the root of the cumulant-generating function H of the increment of the log price process V1. We show that the ruin probability admits the exact asymptotic Cu−β as the initial capital u → ∞ assuming only that the law of VT is non-arithmetic without any further assumptions on the price process. |
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| Bibliography: | Библиогр.: 36 назв. |
| ISSN: | 0949-2984 |