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Pricing And Hedging Of Contingent Claims For The Model Of Exponential Simemartingale

Posted on:2004-06-03Degree:DoctorType:Dissertation
Country:ChinaCandidate:H F YanFull Text:PDF
GTID:1116360122480031Subject:Applied Mathematics
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The mathematical finance is a new intersection subject and receives high attentions ininternational finance and applied mathematics community. The pricing and hedging ofcontingent claims is one of the center problems in this research, which involves themodern asset pricing and portfolio investment of the modern financial theory, andincludes modern mathematical theory, such as stochastic analysis, stochastic control,optimization theory, mathematical statistics and so on. The study of this field not onlyenriches and develops modern finance but also promotes many branches ofmathematical field. The theory of pricing and hedging of contingent claims has a directinfluence on the innovating of financial tool and the effective performance of financialmarket. It also has wide applications to the investment strategy of the company, theevaluation of the research object and the risk management in the financial institution.Pricing and hedging of contingent claims is systematically studied in exponentialsemimartingale model. The fundamental theory of asset price is proved under thismodel. The necessary and sufficient condition of the existence and uniqueness aboutmean-variance optimal and pseudo-locally risk-minimizing hedging strategy is obtained,and the precise expression under the two optimal strategies is given when the market isincomplete with free-arbitrage. When the market has arbitrage opportunity, the actuarialpricing of European option is obtained by using a new pricing method ----actuarialapproach. The main results are listed in the following. The exponential semimartingale model is established in financial market. The necessary and sufficient condition of the existence of the equivalent local martingale measure is given and the first and second fundamental theorems of the asset pricing under this model are proved. The free-arbitrage exponential semimartingale model is constructed. Two sufficient conditions of the existence and uniqueness of mean-variance optimal hedging strategy are obtained in general case. The necessary and sufficient condition of the existence of minimal risk and pseudo-locally risk-minimizing strategy is presented and the sufficient condition of contingent claims having an F-S decomposition is given. In the case that the accumulated gain process is continuous semimartingale, the conditions of the existence and uniqueness of mean-variance optimal hedging strategy is equivalent to the conditions that the variance optimal martingale density of accumulative return process satisfies the inverse Holder inequality. When the accumulative return process is continuous semimartingale and the mean-variance optimal martingale density satisfies inverse Holder inequality, an explicit expression of mean-variance optimal strategy is given, some solutions to optimal problems relative to the rule of square optimization are achieved and the efficient frontier on variance optimal strategy is attained under mean constrained. vA multi-dimension diffusion process model of financial market is researched deeply. We prove that this market model is an incomplete model with free-arbitrage. The characteristics of all the martingale measure are given under this model. A necessary and sufficient condition of the local martingale measure being variance optimal one is acquired. An accurate expression of densities of variance optimal martingale and the minimal martingale are obtained. We get the concrete expressions of the mean-variance optimal strategy in multi-dimension diffusion process and of the risk- minimization strategy. The general stochastic volatility market model is established. The local martingale measure of this model is characterized. We prove that the market model is an incomplete model with free-arbitrage. The minimal martingale measure and the variance optimal one are characterized. We get the R...
Keywords/Search Tags:contingent claim, incomplete market, exponential semimartingale, hedge, mean-variance optimal strategy, risk minimal strategy, actuarial pricing, option pricing .
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