具有复合相依的离散时间风险模型的尾部渐近及数值模拟
Tail Asymptotic of Discrete-Time Risk Model with Compound Dependence and Numerical Simulation
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摘要: 本文研究具有复合相依的离散时间风险模型.保险公司进行风险和无风险投资导致了任意相依的随机折现因子.索赔额服从单边线性过程, 其中噪声项遵循成对渐近独立,噪声项和随机折现因子相互独立. 假设噪声项不必同分布并且是非负的随机变量,其分布分别为F_1,F_2,\cdots,F_n.当平均分布n^-1\tsm_i=1^nF_i是重尾时,本文得到离散时间风险模型的有限时间破产概率的渐近估计.最后通过蒙特卡洛模拟验证了本文的结果.Abstract: This paper considers a discrete-time risk model with compound dependence. The risk-free and risky investments of an insurer lead to arbitrarily dependent stochastic discount factors. The claim-sizes are assumed to follow a one-sided linear process with pairwise asymptotically independent innovations. The innovations and the stochastic discount factors are mutually independent. We assume that innovations are not necessarily identically distributed nonnegative random variables with distributions F_1,F_2,\cdots,F_n. When the average distribution n^-1\tsm_i=1^nF_iis heavy-tailed, we establish some asymptotic estimates for the finite-time ruin probabilities of this discrete time risk model. We demonstrate our obtained results through a crude Monte Carlo simulation.