On risk models under Markovian environments and their applications

马尔可夫环境下的风险模型及其应用

• 批准号: 327003-2009
• 负责人: Lu, Yi
• 金额: $ 1.38万
• 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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=526780
• 关键词: risk; models; under; Markovian; environments

The nature of the insurance business is the promise by the insurer to pay all claims of the insured that are covered in exchange for a policy premium. In addition, the insurer commits some capital (surplus) to assure that the promise will be kept even under special circumstances. We study a portfolio within the insurance company with a positive allocated initial risk reserve (fund) at the beginning of the considered period. The risk reserve is credited premiums with a constant rate and debited amounts of claims due at the time of the arrival. When the claim arrivals are modeled by a Poisson process, the risk reserve process is the so-called classical risk process. We are concerned about the possibility that the insurer does not have enough funds to pay its liabilities (claims), which is the case when the risk reserve falls below zero. More precisely, when this happens we want to know what the odds are for this to happen within a finite time period and what the worse-case scenario would be. These are the basic risk-related quantities of my interest.

保险人对被保险人的保险责任承担的，保险人应当向被保险人支付保险费。此外，保险公司承诺一定的资本（盈余），以确保即使在特殊情况下也能信守承诺。我们研究了保险公司内部的投资组合，在所考虑的时期开始时具有正分配的初始风险准备金（基金）。风险准备金以固定费率贷记保险费，并借记到达时到期的索赔金额。当索赔到达服从泊松过程时，风险准备金过程就是所谓的经典风险过程。我们担心保险公司没有足够的资金支付其负债（索赔）的可能性，这是当风险准备金福尔斯降至零以下时的情况。更确切地说，当这种情况发生时，我们想知道在有限的时间内发生这种情况的几率是多少，以及最坏的情况是什么。这些是我感兴趣的基本风险相关量。