Some Models And Analysis Of Finance And Insurance

The finance and insurance become more and more important with the society forward, therefore their mathematical models and quantitative analysis are especially important. In this dissertation, some stochastic models are studied and the following questions are studied mainly.1. In view of the expand of the insurance company,the discrete risk model with two-type-insurance is established. The defective discrete renewal equation is given. The adjustment coefficient is studied and the ruin probabilities are estimated when the adjustment coefficient exists. The ruin probabilities are estimated by the discrete renewal inequality and this method is applicable to the situation which the adjustment coefficient doesn't exist.2. The Markov risk model with two-type-insurance is constructed, the integral equation of the ruin probability is given;the ruin probabilities are estimated by the general renewal technique;the model is extended to a general case.3. Prom the analysis of the risk model with random incomes, the Markov risk model with Markov random incomes is studied, the integral equation of the ruin probability is given and the probabilities which the incomes and the claims are submitted to exponential distribution and mixed exponential distribution respectively.4. On the basis of the existence of frictions in the financial market, the problem of hedging European Contingent Claims in the market that has frictions in the form of a higher interest rate for borrowing than for lending and percentage management costs for holding or borrowing risk assets is studied. The upper-hedging price and the lower-hedging price of a European Contingent Claim are given, the existence of the optimal upper-hedging portfolio for hedging and the optimal lower-hedging portfolio for hedging are showed and the arbitrage-free interval is obtained.5. The pricing problem of geometric average Asian option with fixed strike price the price process of underlying asset follows a geometric Levy model, the pricing formula of the payoff of geometric average Asian option is derived and the simpler integro-differential equation which the price process satisfies is showed.