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Title: Finite Horizon Trading Strategy with Transaction Costs and Exponential Utility in a Regime Switching Market
Keywords: Exponential Utility, Regime Switching, Penalty Method, Projected SOR Method, Investment, Risk
Issue Date: 17-Aug-2010
Citation: XU SHANGHUA (2010-08-17). Finite Horizon Trading Strategy with Transaction Costs and Exponential Utility in a Regime Switching Market. ScholarBank@NUS Repository.
Abstract: This thesis studies the finite horizon optimal trading strategy with proportional transaction costs in a regime switching stock market. This problem is an extension of the classic investment strategy in a static economic condition. The exponential utility function is considered here. The study of this problem is mainly motivated by Dai et. al. (2010), in which the finite horizon optimal investment problem with proportional transaction costs under logarithm utility function in a regime switching market is studied. In this thesis, we use dynamic programming approach to derive the Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions. For our exponential utility case, the transformation is different from the one in the logarithm utility case, and we will get a system of variational inequalities with gradient constraints. For the power utility case, there is also a similar system with gradient constraints. The difference lies in that the case with exponential utility cannot lead to a self-contained system of double obstacle problems. Due to the fact that no closed-form solution exists, we employ two numerical methods, namely the penalty method and the projected SOR method to solve the system of variational inequalities based on certain assumptions. Finally we show the optimal trading strategies.
Appears in Collections:Master's Theses (Open)

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