| In the category of financial mathematics and insurance mathematics, ruin theory is the core of risk theory. As a special organization who deals with risk, insurance company surely meets risk in its business, as such, it’s very important to research on this subject. To the aim of increasing insurance company’s payment ability and to make sure it can operate stably, scientific forecasting of insurance premium income, the future possible claims and estimating ruin probability of the company are very important.In the business of an insurance company, on one hand it takes advantage of income to produce profit, on the other hand it should remain some money in case of claims coming. Less remaining money increases risk, while an inappropriate investment portfolio affects the efficiency of money. In this thesis we solve the problem from the view of ruin probability, and help companies to make an investment strategy. We consider that the reserve of an insurance company follows a Cramer-Lundberg process. The company invests its income into one risky asset and one riskless asset. Suppose the claim size distribution is given, the HJB equation is applied to minimize the ruin probability of the insurance company. The capital amount and optimal portfolio, anyone is known, the other one can be determined. The optimal investment strategy is obtained through numerical algorithm which avoids the difficulty in solving high ordered equations. Finally, we discuss how different strategies influent the ruin probabilities. These results can be applied in actual operations.In the last chapter, We change the premium process into a compound Poisson model, give out the estimation of ruin probability and induce the formula of insurance price by using this new model with two compound Poisson models, especially in the exponential case. This method can be applied to company operation. Meanwhile, we conclude that either raising insurance price or broaden business size can not reduce ruin probability efficiently. |
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