A Study On The Optimal Investment Strategies Of Insurance Company In Markovian Environment

With the development of economic globalization and rapid exchange of information,people have a deeper understanding of risk,discussing how to choose insurance companies to buy insurance has become a common problem.Therefore,insurance companies have flourished in recent years.As a profitmaking organizations,protecting customers and making profits are their objective,that charging premiums is not enough.Insurance companies must think how to choose appropriate investment strategies to improve the profitability of the company in combination with the economic market.For the economic market,Markovian adjusted financial insurance model seems to be more suitable for the real financial insurance data than the classical financial insurance model,that is to say,Markovian adjustment financial market model is better than other common financial market models.In the risk theory,Markovian adjusted risk model has a advantage that insurance companies can adjust their own insurance policies with the change of external environment(weather,economy,government policies,etc.).For finding the optimal investment strategy,maximizing the expected utility wealth or minimizing the ruin probability becomes the main problem of insurance companies.Based on the above background and the more and more important role of Markovian regulation model in financial insurance,this paper studies the optimal investment strategy under the exponential and logarithmic utility functions of an insurance company in Markovian Environment.In order to fit the risk model more closely in practice,this paper assumes that the risk process of an insurance company is described by ?0) process,according to the standard of maximizing the expected utility function of terminal wealth,insurance companies manage their own risks by controlling the number of policies sold.This paper constructs an incomplete economic market model under the environment of Markovian,so this paper builds a family of Markovian modulation measure transformation to solve the Markovian property in the economic market model by constructing the product space,by using the method of minimum maximum martingale measure to solve the incompleteness in the economic market model,and the explicit solution of the optimal investment strategy of insurance company under two utility functions is derived.