The ruin probabilities of a discrete time risk model with one-sided linear claim sizes and dependent risks. (English) Zbl 1390.91197
Summary: This article investigates the ruin probabilities of a discrete time risk model with dependent claim sizes and dependent relation between insurance risks and financial risks. The risk-free and risky investments of an insurer lead to stochastic discount factors \(\{\theta_n\}_{n\geq 1}\). The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations \(\{\varepsilon_n\}_{n\geq 1}\). The i.i.d. random pairs \(\{(\varepsilon_n\theta_n)\}_{n\geq 1}\) follow a common bivariate Sarmanov-dependent distribution. When the common distribution of the innovations is heavy tailed, we establish some asymptotic estimates for the ruin probabilities of this discrete time risk model.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
asymptotic estimate; bivariate Sarmanov distribution; dependent insurance and financial risks; heavy tail; one-sided linear process; ruin probabilityReferences:
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