Stochastic approximation is one of the oldest approaches for solving stochastic optimization problems. In the first part of the dissertation, we study the convergence and asymptotic normality of a generalized form of stochastic approximation algorithm with deterministic perturbation sequences. Both one-simulation and two-simulation methods are considered. Assuming a special structure on the deterministic sequence, we establish sufficient conditions on the noise sequence for a.s. convergence of the algorithm and asymptotic normality. Finally we propose ideas for further research in analysis and design of the deterministic perturbation sequences. In the second part of the dissertation, we consider the application of stochastic optimization problems to American option pricing…

Author: Xiong, Xiaoping

Source: University of Maryland

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