Ruin Model In Delayed Payment

The ruin theory is a major research topic in risk theory. The classical ruin model does notconsider interest rates, investment returns, inflation, operating expenses, policyholderdividends and some other factors.In real life, the insurance companies can always find a variety of reasons to delay thepayment of insurance in our claims. In other words, the actual time of insured person’s claimand the paid time of insurance company are often inconsistent. This behavior of insurancecompanies is actually improving their revenue, and reducing their risk in disguised form.Certainly, we do not encourage that behavior, but without considering the credibility andintegrity of the insurance companies, this paper will focus on how the actuary behavior affectsthe ruin probability of insurance companies.The classical ruin model usually assumes that the number of claims process in line withthe number of Poisson Process, and the waiting time between two events in line with theexponential distribution. This paper will improve this condition, so that the incident adds adelay in the arrival time of payment, making the process more in line with the number ofclaims process to some of the actual behavior in insurance payment. This paper firstintroduces some of the major theories and research in the classical ruin model briefly, andexplains specifically how to establish an appropriate ruin model considering the factors of thedelayed payment of insurance companies. According to the delay behavior of insurancecompanies, we will discuss the delayed time in three cases. Among them, the former twocases are more specific. Respectively, we will discuss how to express the delayed-paymentruin probability by the adjustment coefficient in both cases, as well as the relationshipbetween the delayed-payment ruin probability and the classical ruin probability; when theclaim amounts are exponentially distributed, we will give the direct expression of thedelayed-payment ruin probability. In the third case, where the delayed time complies withgeneral distribution under certain assumptions, we will give the calculus equation satisfied bythe delayed-payment ruin probability, and will use it to verify the former two cases. In the lastpart of this paper, we will use the actual data to calculate the delayed-payment ruin probability,and compare with the classical ruin probability, pointing out that the lowering effect of the actual delay payment behavior to the ruin probability.