Capital Requirement and Allocation for Insurance Companies by the Co-TailVaR-Based Insolvency Exchange Option Method

Determining the total capital requirement and allocating capital to business lines are two key parts of financial and risk management for a multi-business insurance company. Several well-known methods have been proposed to calculate these qualities. Our paper considers the total capital requirement for a multi-business insurance company based on Co-TailVaR from each line level to the entire company level. The benefits of diversification are considered in turn. Following the Myers-Read method, we initially allocate the total capital to each line by equalizing the marginal insolvency exchange option value. Then we apply some specific rules to obtain the weighted capital that should be allocated to each line. We also propose a Co- TailVaR-based insolvency exchange option method in which the total requirement of capital is determined by each linepsilas risk and the diversification benefit. Furthermore we take both each linepsilas risk and each linepsilas contribution to the entire company insolvency as factors determining the capital allocation. Such capital allocation has the property of ldquoadding up.rdquo At last we provide a detailed example to illustrate our method.