Optimized Economic Capital Allocation Model And Its Application

Insurance companies holding capital is not only because they are obligated by regulators to hold capital, but also is to protect the company form insolvency and ensure the future of the company as a going-concern. While it is desirable that it holds large amounts of capital, usually this does not come without cost. So, how to determine the aggregate capital and how to allocate the aggregate capital to its business units appropriately is generally concerned by insurance companies.Our thesis is mainly divided into two parts, the theoretical research and the empirical analysis.To the theoretical research, we will study how to determine the aggregate capital and how to allocate the aggregate economic capital of financial firm to its business units. To the first problem, we give the definition and calculation of it under the risk measure functions. Then, to the second problem, we solve it by steps. First, we propose to formulate an allocation criterion, that is capital should be allocated such that for each business unit the allocated capital and the loss are sufficiently close to each other. Under this criterion, we formulate an optimal capital allocation model, thus the capital allocation problem is transformed into solving the optimal capital allocation model. By giving the deviation measure function a specific form, such as a quadratic function, and then we get the quadratic allocation problem. And, we give the general solution of this problem. Furthermore, by choosing two different forms of the parameter in the model, we get two different forms of the allocation solutions, called business unit driven allocations and aggregate portfolio driven allocations respectively.To the empirical analysis, we choose the aggregate portfolio driven allocation to analysis and the firm which we will analysis is CICC P&C. By assuming the random vector consisting of the business units’loss follows a multivariable elliptical distribution and giving two different forms of the parameter in the model, we have deduced two different forms of the allocation models. And we use these two models to do the empirical analysis. First, we measure the correlation coefficient cross the business units by formulating multivariable Copula models. By estimating the parameters in the Copula models, we get the estimated correlation coefficient matrix. After that, based on the formulated Copula models, multivariable normal Copula and multivariable student t-Copula, we use Monte Carlo Simulation to calculate the aggregate economic capital of the firm. Last, for each of the two calculated aggregate economic capital under different Copulas, we use the two models to calculate the allocated capital to every business unit of the firm respectively. We show that allocated capital under the student t Copula can catch the business units loss’s fat tail much better. Therefore, our optimal economic capital allocation model is useful and meaningful for the insurance firms to decide how to allocate the economic capital.