The Application Of Martingale In Actuarial

In insurance actuarial, ruin theory is the important part of insurance actuarial; the coreissue of the ruin theory is to use the ruin probability to measure the operations of insurancecompanies. Actually, the probability which the company’s surplus funds is negative isknown as ruin probability, ruin probability can be used as a basis for risk assessment ofinsurance companies; It plays a very important role in guiding the insurance companies andinsurance supervision department. Martingale is a stochastic process theory tools which, inrecent years, as a powerful research tool, gradually infiltrate the various disciplines.Therefore, it has high practical value to use the martingale in actuarial risk models.This paper can be taken into two parts. In first part, In ruin theory,we often do notconsider the interest rate, or just consider the ruin problem under the constant interest rate.But in fact, due to the impact of external economic factors, stochastic interest rate are closerto the fact. The paper discusses the ruin probability of insurance company, which usemartingale theory to obtain the exponential upper bound of the final ruin probability withstochastic interest rate.In second part, using the martingale theory to get the upper bound of the ruinprobability, the bankruptcy probability is acted as a criterion by the insurer, making theirown risk reaches a minimum through reinsurance strategy, describing the aggregation ofrisk through the update process, the upper bound of the ruin probability is given by theadjustment coefficient, adjustment coefficient can be regarded as a function of the excess ofloss reinsurance retention, drawing against the insurer’s optimal retention level afteranalyzing the function, making the upper bound of the ruin probability a minimum.