Optimal Reinsurance Policy For Two Types Businesses Under The VaR Risk Measure

In this dissertation,by the limitation of maximum risk measured by VaR,it discusses the optimal proportional reinsurance policy of an insurance company in the case of two risk independent businesses and two risk dependent businesses,with the allowance of insurance company to invest in capital market between risk-free assets and risk investment portfolio.It applies two different premium principles to two businesses according to the volatility of compensation.If variance of compensation is small,the premium is calculated in expect premium criterion.Otherwise,it is calculated in standard deviation premium criterion.Hence,it calculates the terminal wealth and optimal retention rate by means of existed study framework.It draws the following conclusions.Conclusion one: the terminal wealth and optimal retention rate is decided by maximum risk faced by insurance company,the mean value and variance of return rate of underwriting and investment portfolio,and it is independent of the premium principle.Conclusion two: standard deviation premium criterion is more suitable than expectation in the way of measuring the volatility of compensation.Conclusion three: for single business model,optimal retention rate has a negative relationship with mean value of compensation under the expectation premium principle,and has a positive relationship with mean value of compensation and has a negative relationship with variance of compensation under the standard deviation premium criterion.As for two businesses model,if the optimal retention rate goes in same direction with variance of compensation(only one business is applied by standard deviation premium criterion),the optimal retention rate goes in same direction with the variance of second business compensation;If the optimal retention rate goes in same direction with variance of compensation and the variance of the second business compensation is same,the bigger the variance of the first business compensation,the bigger the optimal retention rate,vice versa.Conclusion four: competed to independent risk cases,the optimal retention rate of dependent cases would be affected by the common factors which have a result in the number of compensation.