Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments
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Abstract
Consider a general bivariate Lévy-driven risk model. The surplus process Y , starting with Y 0 = x > 0, evolves according to d Y t = Y t - d R t -d P t for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x →∞, which confirms Paulsen's conjecture.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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