Optimal Economic Capital Allocation For Underwriting And Investment Risk In Property And Casualty Insurance Company

Much more competitions in insurance market and increasingly complication of finance products weaken solvency and capital adequacy capability of insurance companies. Statutory solvency capital requirements only just protect capital adequacy ratios in the lowest level, while also does not include the influence of investment risks and investment structures. Without considering self-businesses portfolio and overall objective, insurance companies will have difficulty in keeping stability, obtaining long-term development and profitability even basing on these regulatory requirements.Under the situation mentioned above, the paper establishes a model for research objects-underwriting and investment risks, aiming to make the optimal decision for company operation. The optimal decision is the one which meets solvency risk capital requirement and also creates the biggest profit for company. In addition, it reveals the correlationship among risks and proves diversification in company portfolio based on Copula functions, and promotes an advanced model ground on "Mean-Variance" model by Markowitz, which uses Copula-Kendall's tau for portfolio efficiency frontier. At last, the paper chooses maximizing RAROC as the benchmark for economic capital allocation.To better illustrate risk correlation, the paper uses two different parameter methods to find the fitting copula functions for loss ratio on insurance business and rate of return on investment. In the meantime, it simulates large numbers of data by Monte Carlo, analysis relationship between insurance and investmet business and compares linear correlation to Copula Kendall's tau. When calculating RAROC, it uses coherent risk measure CVaR to evaluate economic capital amount so as to to balance risk and return.This paper carries on research from three aspects:from the angle of regulation, it allocates economic capital for both insurance and investment business, which overcomes the deficiency in premium-based capital requirements; for the operation goal, it promotes operation decisions satisfying solvency capital requirements for underwriting and investment business with the target of shareholders value maximum, that is maximum RAROC; considering capital allocation technology, it integrates different risks by copula function and measures the amount of risks by CVaR which means much more accurate risk measurement for expected return.