简介

My research lies in the fields of Probability and Stochastic Processes. In particular, I am interested in applying Large Deviations Principles (LDP) to problems from Mathematical Finance regarding portfolio choice, derivative contract valuation, and large investor analysis. The portfolio choice research concerns the optimal investment problem in the limit of a long horizon. The goals are to identify the long-run optimal strategy, prove convergence of finite horizon optimal strategies to the long-run strategy, and use the long run strategy to illuminate relationships between investor preferences, economic factors and dynamic asset demand. Regarding derivative contract valuation, my research focuses on two separate problems. The first involves identification of the distribution of a perpetuity contract and the second problem concerns efficient pricing of path-dependent options in stochastic volatility models via Importance Sampling. The large investor analysis centers on two questions. First, how should investors with large positions price contingent claims? Second, why would an investor take a large position in a contingent claim? The first problem involves approximating utility indifference prices in the limit of a large position size. Such approximations offer a natural counterpart to small claim approximations, which exist in the literature, though the analysis is significantly different, since in the large claim setting the market must vary jointly with position size. The question of why one would become a large investor is of great importance given the massive increase in notational amounts outstanding of derivatives contracts in recent years. Here, the research seeks identification of both investor and market characteristics under which large positions arise endogenously.