New directions in insurance loss modeling, ruin theory and their applications

该研究项目继续在数学风险理论中寻找新的理论和实践成果，将该领域与其他保险或金融领域联系起来，如保险损失建模，索赔准备金和操作风险管理。现实的情况下，考虑两个或两个以上的保险公司在同一时间发挥作用。对于再保险人承担部分保险人损失的情况，或者两个或两个以上保险人试图确定最佳风险分担策略以最大限度地减少某些风险措施的情况，将进行详细讨论。已发生但未报告的损失准备金和已报告但未结算的准备金是索赔准备金中的重要量，并将通过经典的破产相关度量-破产时间，破产前盈余和破产时赤字-纳入保险公司的盈余分析。从更实际的角度来看，对精算师来说，保险损失建模是最具挑战性的问题之一。在这个建议中要解决的一个重要问题是确定潜在的候选人，可用于处理截断和删失数据集时拟合损失量。由于其非常吸引人的特性（密集，封闭等），混合的Erlang分布类将在开发基于公知的EM方法的几种拟合算法中起主要作用。将详细研究所提出的基于Erlang的方法在索赔准备金中的潜在应用。金融机构面临着各种风险，如战略风险、声誉风险、市场风险、信用风险、业务风险、操作风险、流动性风险等，其中市场风险、信用风险和操作风险在实践中是很容易量化的。在本项目中，我们感兴趣的是根据巴塞尔II指令中提出的高级度量方法（AMA）来度量操作风险。为了避免模拟，我们有兴趣找到封闭形式的分析解决方案，与操作风险相关的整体损失的分布，考虑到某些依赖结构，可能会发生在不同的测量单位。

This research project continues the search for new theoretical and practical results in mathematical risk theory, connecting the area with other insurance or financial areas, such as insurance loss modeling, claim reserving and operational risk management. Realistic scenarios are considered when two or more insurance companies are at play at the same time. Situations where a reinsurer covers parts of the insurer losses, or where two or more insurers try to determine an optimal risk-sharing strategy that minimizes certain risks measures, will be pursued in details. The incurred but not reported loss reserve, and the reported but not settled reserve are important quantities in claim reserving, and will be included in the analysis of the surplus of an insurance company via its classical ruin related measures - the time to ruin, the surplus prior to ruin and the deficit at ruin. On a more practical side, modeling insurance losses is one of the most challenging problems for actuaries. An important question to be addressed in this proposal is the identification of potential candidates which can be used for fitting loss amounts when dealing with truncated and censored data sets. Due to its very appealing properties (denseness, closure etc.), the mixed Erlang class of distributions will play the main role in developing several fitting algorithms based on the well-known EM method. Potential applications of the proposed Erlang based methods in claim reserving will be studied in detail. Financial institutions are exposed to a variety of risks such as, strategy risk, reputation risk, market risk, credit risk, business risk, operational risk, liquid risk, and so on. Among these risks, market, credit and operational risks can be easily quantified in practice. In this project we are interested in measuring the operational risk according to the Advanced Measurement Approach (AMA) proposed in the Basel II directive. In order to avoid simulation, we are interested in finding closed form analytic solutions for the distribution of the overall losses associated to the operational risk, taking into consideration certain dependence structures that may occur among the different units of measurement.