On the ordering for the surplus process perturbed by diffusion

受扩散扰动的剩余过程的有序性

• 批准号: 311829-2008
• 负责人: Tsai, ChiLiang
• 金额: $ 1.02万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=396514
• 关键词: ordering; surplus; process; perturbed; diffusion

Stochastic orders and their applications have been proposed in the past decades in a variety of areas of finance, probability and statistics. Ordering can give powerful approximation methods and bounds in situations where realistic stochastic models are too complicated for treatment. In this case, finding well-adapted orders which lead to tight bounds and good approximations becomes an important issue. Stochastic orders are also useful when the underlying distributions are only little known. Among these actuarial applications, ruin is a very important issue for insurance regulators, policyholders and shareholders. Ruin probability can serve as an indicator of an early warning system for potential insolvency. A high probability of ruin might require the insurer to raise premiums, increase the initial capital, or avoid taking the underlying claim amount risk. In this project, I would like to study stochastic orders for pairs of ruin probabilities and relevant actuarial quantities (including the deficit at ruin and the mean time to ruin, etc.) resulting from two claim size random variables with unequal premium rates, expected claim frequencies and claim severities, relative security loadings for corresponding two surplus processes perturbed by diffusion. These ordering relationships can also be used to obtain feasible upper and lower bounds on the underlying actuarial quantities. Thus, ordering pairs of ruin probabilities can help the actuary make the right decision: i.e., other business considerations being equal, taking the kind of risks yielding the lower ruin probability.

在过去的几十年中，在财务，概率和统计数据的各个领域都提出了随机命令及其应用。在现实的随机模型过于复杂而无法治疗的情况下，订购可以提供强大的近似方法和边界。在这种情况下，找到适应良好的订单，导致紧密的范围和良好的近似值成为一个重要问题。当基础分布仅鲜为人知时，随机顺序也很有用。在这些精算应用中，对于保险监管机构，保单持有人和股东来说，废墟是一个非常重要的问题。破坏概率可以作为潜在破产的预警系统的指标。毁灭的可能性很高可能要求保险公司提高保费，增加初始资本或避免承担基本的索赔金额风险。在这个项目中，我想研究一对破坏概率和相关精算量的随机订单（包括毁灭性的赤字和平均毁灭的赤字等），这是由于两个索赔规模的随机变量不平等的溢价，预期的索赔，这是两个索赔规模随机变量导致的频率和声明严重性，相对的安全载荷，用于相应的两个剩余过程受到扩散的干扰。这些有序关系也可用于在基础精算量上获得可行的上限和下限。因此，订购一对废墟概率可以帮助精算师做出正确的决定：即，其他业务考虑是平等的，以降低毁灭概率的风险。