Stochastic Claims Reserving Method Based On Claims Development Triangles With Individual Data

Insurance company as a special industry managing risk, its solvency is an important indicator to measure the viability of the company. To ensure the interests of policyhold-ers, solvency is strictly supervised by many countries. Outstanding claim reserves, the main liabilities of non-life insurance company, have a very important influence on oper-ating conditions and solvency. Outstanding claim reserves which are calculated through scientific actuarial method can objectively reflect the solvency of insurance company, im-prove regulatory efficiency, and also help insurance company-correctly understand its operating conditions and improve management efficiency.The most simple and practical methods to estimate outstanding claim reserve are chain-ladder method, and some stochastic methods extending out from it, such as Mack model, generalized linear model, bayesian model and so on. As a deterministic assessment, chain-ladder method can only give an estimate of outstanding claim reserve, but it is difficult to say how accurate the value is. At this stage, various actuarial methods to calculate outstanding claim reserve cover a few delayed years, so they can not reflect the feature of "long tail" insurance.In this case, it's make more sense to use a random model. But all of these methods are based on aggregate data. Aggregate data in claims development triangles is the sum of all individual data of a single time period, and thus some useful information will be inevitably lost. This results that traditional model of aggregate data doesn't make full use of complete information provided by historical data to effectively predict the reserves. This paper studies a stochastic model based on claims development triangles with individual data, which makes full use of data of every policy to assess loss reserve.The paper is divided into three parts. Part I introduces some existing methods briefly. Part II presents a stochastic model based on claims development triangles with individual data, which estimates the distribution of the number of IBNR claims and RBNS claims. The third part calculates the distribution of compensation for each claim, and then calculates the distribution of loss reserve. The innovational points of this paper are that, delayed reporting time and adjustment time are applied to construct a stochastic model to estimate the distribution of number of IBNR claims and RBNS claims. Not only the distribution of loss reserve can be got, but also the point estimate of each year's reserve in lower triangular can be calculated.