| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 89 === We will consider the Backward Stochastic Differential Equations and their applications in the financial models. The BSDEs were introduced by Pardoux and Peng, 1990 and the financial models were developed for a long time since Black and Scholes, 1973. In this paper, we summarize the BSDEs theory due to Peng and the financial models due to Karatzas. The pricing models in the complete financial markets under two hypotheses will be introduced. These two hypotheses were both given by Karatzas, 1987 and 1997. The hypothesis in 1987 is a special condition of the hypothesis in 1997, but under it the market has the property of the uniqueness. Then we will apply the BSDEs theory in other two constrained market models under the former hypothesis. One is the pricing in a complete market where the borrowing interest rate is more than the risk-free rate, and the other is the hedging in a incomplete market.
In chapter 1, we will introduce the financial market models due to Karatzas, 1997 and make a little change in his original
assumptions and definitions. In chapter 2, we introduce the BSDEs theory and apply them in proving the property of the uniqueness under the hypothesis in 1987. The pricing under the constrained condition and the hedging in the incomplete market are also in chapter 2. Finally in chapter 3, we make some conclusions.
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