Ruin probabilities for a Lévy-driven generalised Ornstein-Uhlenbeck process
| Autor: | Serguei Pergamenshchikov, Yuri Kabanov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
050208 finance 05 social sciences Ornstein–Uhlenbeck process Function (mathematics) Орнштейна-Уленбека-Леви процесс 01 natural sciences Lévy process 010104 statistics & probability Capital (economics) 0502 economics and business Applied mathematics Initial capital авторегрессия со случайными коэффициентами теория обновления 0101 mathematics Statistics Probability and Uncertainty Finance Mathematics |
| Zdroj: | Finance and stochastics. 2020. Vol. 24, № 1. P. 39-69 |
| Popis: | We study the asymptotics of the ruin probability for a process which is the solution of a linear SDE defined by a pair of independent Levy processes. Our main interest is a model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let $\beta >0$ be the root of the cumulant-generating function $H$ of the increment $V_{1}$ of the log-price process. We show that the ruin probability admits the exact asymptotic $Cu^{-\beta }$ as the initial capital $u\to \infty $, assuming only that the law of $V_{T}$ is non-arithmetic without any further assumptions on the price process. |
| Databáze: | OpenAIRE |
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