Dynamical Linear Model For Estimating Outstanding Loss Reserve Under DFA Framework

Dynamic Financial Analysis (DFA) is a new tool that can help insurance company manager to evaluate risk and make strategy management. Casualty Actuarial Society (CAS) has classified it as: "a systematic approach to financial modeling in which financial results are projected under a variety of possible scenarios, showing how outcomes might be affected by changing internal and/or external conditions." DFA model includes three major parts: stochastic scenario generator produces realizations of random variable representing the most important drivers of business results, financial risk, economic results. The output is the input information of capital model and liability model. The output of capital model and liability model can then be analyzed by management in order to improve the strategy, i.e. make new strategic assumptions. This can be repeated until management is convinced by the superiority of a certain strategy.Part of DFA exercise is not only estimating reserve, but also quantifying reserving risk, and to do this, it is necessary to have a model that simulates the likely payment of outstanding liabilities. Outstanding loss reserve is the major liability in insurance company's balance sheet. Because traditional reserving methods can not provide the precise of reserving, stochastic reserving methods are used in DFA to provide the estimate of reserve variability, not only in the reserve estimates themselves.There is the link between the chain ladder model and stochastic reserving method. Stochastic chain ladder model that is on the basis of the chain ladder model can provide the precise of reserving and estimate of reserve. In order to use the information in the history data, Bayesian theory was introduced to the estimate of model's parameters. Dynamical linear model includes state space model and system equation on the basis of stochastic chain ladder. Dynamical linear model is solved by Kalman filter. The precise of Dynamical linear model's result is better than the stochastic chain ladder's. This is because the prior information gave tight estimates of the parameters.The paper describes the principle and framework of DFA, the requirement and method of outstanding loss reserving in DFA, and stochastic reserving methods. This paper also shows how build Dynamical linear model on the basis of stochastic reserving method and Kalman filter. Finally the paper gives a numerical illustration, the data that is from our country casualty insurance company. The results show that Dynamical linear model can meet the requirement of outstanding loss reserving in DFA,...