The Research On The Estimation Of The Risk Margin Based On The Equivalent Martingale Measure

The concept of risk margin is proposed in Solvency Ⅱ, it is one of the most complex concepts in the actuarial world.Risk margin is produced under the theory of market-consistent valuation,it is an important part of the reserve liabilities, assessment of reserve liabilities depends largely on the understanding and evaluation method of the risk margin, also risk margin is an important content of the insurance company risk management, so accurate understanding and choosing the appropriate evaluation method of the risk margin has very important theoretical and practical significance.In actuarial practice, the valuation of the risk margin is often not based on a sound model,but various simplified methods are used,the most commonly used method are the quantile method and cost of capital. The quantile method is easy to understand, but it does not conform to the measurement requirements of market consistent valuation.The difficult of cost of capital is that almost every case is not tractable,the calculations of solvency capital requirement (SCR) is based on various quantifiable risk,this is unable to deal with in the actual application,so often use a variety of proxy.Therefore, the actuarial field need not only accepted definition of the risk margin, but also need put forward some practical and reasonable method to estimate the risk margin.In this paper,we first make clear several understanding of the concept to the risk margin,also introduce the four kinds of methods to calculate the risk margin in actuarial field.Then briefly introduces the theory and method of the equivalent martingale measure,this paper apply the equivalent martingale measure to estimate the risk margin.Finally introduce a specific evaluation method to the risk margin from the aspect of theory which belongs to modified assumptions methods——the estimation of the risk margin based on the equivalent martingale measure.Under Bayesian log-normal chain ladder model,we get the estimation result of the risk margin through two kinds of calculation methods which are analysis and simulation, by comparing the calculation results,we study the differences of the methods to evaluating the risk margin, enriches the theory and method of risk margin assessment in the actuarial field.