Asymptotic estimates for finite-time ruin probability in a discrete-time risk model with dependence structures and CMC simulations

Abstract

Consider a discrete-time risk model with dependence structures, where claim sizes are assumed to follow a one-sided linear process whose innovations further obey a so-called bivariate upper tail independence. The stochastic discount factors follow a stationary causal process. Then, the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risks, i.e. the insurance risk and financial risk. The two kinds of risks form a sequence of independent and identically distributed random pairs which are copies of a random pair with a common bivariate Sarmanov dependent distribution. When the distributions of the innovations belong to the intersection of the dominated-variation class and the long-tailed class, we derive some asymptotic formulas for the finite-time ruin probability. We also get conservative asymptotic bounds when the distributions of the innovations belong to the regular variation class. Finally, we verify our results through a Crude Monte Carlo simulation.

Keywords:

• Bivariate Sarmanov distribution
• dependent insurance and financial risks
• finite-time ruin probability
• stationary causal process
• heavy-tailed distribution
• one-sided linear process

Subject classification codes:

• 62P05
• 62E20

Acknowledgments

The authors wish to thank the referee and the Editor for their very valuable comments on an earlier version of this article.

Additional information

Funding

The article is supported by the National Natural Science Foundation of China (No.71871046, 71501025).