Research On Reserving Risk Based On Bayesian Bootstrap Method

The main risks from insurance companies consist of underwriting risk, operational risk, defaulting risk, underwriting risk includes reserve risk and premium risk. Due to the uncertainty of the future payment, the assessed reserves fluctuate around the true value. In order to hedge against the uncertainty of future payment, the insurance companies add an additional part to the technical reserves as a composition of the solvency capital requirement, which is called reserve risk. Reserve risk is to deal with this situation that the reserve is not sufficient to meet the payment and is the measurement of the gap between reserves and future claims. The usual reserve risk is meant for the ultimo risk, the risk in the full run-off of the liabilities. In stochastic models, we can use the root mean square error to measure it. In EU Solvency II, one-year non-life reserve risk was proposed. One-year reserve risk to cover the inadequacy over the next 12 months, the time range is set to be 1 year. One-year reservfe risk is often lower than the ultimo risk, and also more accurate, more conducive to risk regulation.There are analytical method and stochastic models to measure ne-year reserve risk. Wuthrich (2008) first introduced analytical method to measure the one-year reserve risk based on Mack model. However, the analytical method is complex and failing to consider the tail factor. Stochastic Re-reserving method (Ohlsson&Lauzeningks.2009) was produced to overcome the shortcomings. The instruments for Re-reserving method consist of MCMC method and Bootstrap.This paper describes the background of the EU solvency â…¡, and then clears the concept of a one-year reserve risk; then introduces analytical method and Re-reserving method. Then in the context of the Re-reserving method, expand the Bootstrap method into Bayesian Bootstrap method with the consideration of including the tail factor, and we can get the VaR value of the claim development result with the confidence of 99.5% to measure reserve risk. Finally, we use the data from Wuthrich (2008) as an example, and compare the results of the Bayesian Bootstrap method, Bootstrap method and M & W method.We can conclude that the results of Bayesian Bootstrap method are similar with that of M & W method, and smoother than Bootstrap method with lower process error and the estimation error.