The Properties And Applications Of Negative Risk Model And Its Generalized Model

The risk theory is the important branch of Actuarial Science, Which is used ininsurance,finance,securities and investment. The risk theory recurs probability theoryand random process theory to establish mathematics model, which is used to describedifferent kinds of risk process. And ruin theory is the core of risk theory. The ruinprobability can provide an early alarm for decision maker of insurance companies;moreover, it is a very important standard of measuring finance risk to companies. Thereby,the study of ruin probability has the extremely important guiding sense not only tomanaging of insurance companies and supervising of insurance surveillance departments,but also to the stability of financial market.With the development of insurance, a new type of risk process was appeared, whichis different from the classical risk process, it is called negative risk process. In thebeginning of the paper, we introduced the basic negative risk model. Then we generalizedthe model reasonably, and studied its properties and ruin probability. This article containsthe following details:Firstly, by using the definition and properties of the moment generating function, wediscussed main properties of the negative risk process under two conditions: when theclaims number is a constant in a unit time and when the claims process is a compoundPoisson process. We also derived the expression of the ruin probability.Secondly, we generalized the basic negative risk model with constant interest,disturbance item and investment, then analyzed the effect of factors. We derived theexpression of the ruin probability by using the martingale method, and obtained theexpression of expenditure per unit time via the exponential principle.At last, through numerical examples we analyzed the effect of factors to the ruinprobability upper bounder which in the basic negative risk model and its generalizedmodel, and drew the curve chart. In the negative risk model with investment, we are usingthe stochastic control theory in order to make the ruin probability being least in a finitetime.