The Study Of Adjustment Coefficient Under Several Risk Models

As an important branch of actuarial science, risk theory is the focus of the actuarialcommunity’s research and has been widely used in insurance, investment and otherindustries by risk managers and risk decision-makers. As the core of risk theory,bankruptcy theory has important guiding significance in the stability analysis of the riskmanagement process that will occur. So the study of the ruin probability of risk model isthe forceful guarantee of maintaining the entire financial market.Classical risk models have given expressions of ruin probability, and the expressionscontain adjustment coefficient. So, in order to determine or estimate the ruin probability,we must first study on the adjustment coefficient. So based on the definition ofadjustment coefficient, adjustment coefficient under different kinds of risk model isstudied.Firstly, under two risk models, the effects of correlation between insurance premiumarrival process，claim arrival process and distracter on the adjustment coefficient areresearched. According to the related factors，four kinds of situations are obtained. Usingthe method of comparing functions, the size of the adjustment coefficient relationshipunder four situations is obtained. Through the Lundberg inequality, the effect ofcorrelation to Lundberg index is given. Finally, for insurance company, the more risks itmanages and the more risk factors between risks, the easier it will be bankruptcy.Secondly, a new n-fold risk model is introduced, where the claim process is ap-thinning process of the premium arrival process, this means that when premiumhappens then claim will happen in p probability. Using the related properties of thecompound Poisson process and martingale theory, the equation on adjustment coefficientis obtained. In addition, a method for proving the upper and lower bounds of theadjustment coefficient is given, the general expression and the upper bound of thebankruptcy probability under new model are obtained.Finally, a risk model is studied, where the random insurance premium andreinsurance is considered. Upper and lower bounds of adjustment coefficient under thismodel are proved. According to the equation on adjustment coefficient, the relationship between adjustment coefficient and reinsurance coefficient when insurance premiumamount and claim amount obey exponential distribution is given.