Backward Stochastic Differential Equations in Economics and Finance.
详细信息
文摘
My doctoral dissertation looks at the applicability of BSDE backward stochastic differential equations) in economics and finance. In short,a theory of BSDE solves a boundary value problem for the evolution of a stochastic process,given a terminal condition for the process. Since the theory of BSDE has recently introduced to economics and finance,while it has been developed in stochastic control theory for twenty years,the thesis investigates how theory of BSDE can be applied to various models of economics and finance by providing some examples of BSDE from the literature. Another focus is on proposing an alternative algorithm for pricing path-dependent American options,inspired by the numerical techniques developed for BSDEs. While the traditional method to price path-dependent American option is to transform it into a path-independent option,by the technique of state augmentation,the thesis uses Monte-Carlo regression-based method for BSDE to exploit the intrinsic advantages of a path-dependent model. In doing so,a backward control variate is first introduced,which approximates the conditional expectation of the option value by using the analytical scheme to solve BSDE. Second,rather than regressing the option value on basis functions,we perform at each inductive step of the dynamic programming algorithm a sequential regression of the backward control variate. Ultimately,the dissertation demonstrates that the accuracy of the estimator constructed by regressing the backward control variate is superior to the accuracy of the estimator constructed by regressing directly the option value because the backward control variate has overall a smaller variance than the option value.