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Title: Two free boundary problems in optimal investment
Keywords: Optimal stopping, Singular control, Penalty Method
Issue Date: 12-Feb-2009
Citation: ZHONG YIFEI (2009-02-12). Two free boundary problems in optimal investment. ScholarBank@NUS Repository.
Abstract: We have considered two free boundary problems in optimal investment. Problem I is concerned with the optimal decision to sell or buy a stock in a given period with reference to the ultimate average of the stock price. This is an optimal stopping time problem which can be formulated as a variational inequality problem. We provide a partial differential equation (PDE) approach to study the optimal strategy. Problem II concerns numerical solutions for the continuous-time portfolio selection with proportional transaction costs which is described as a singular stochastic control problem. The associated value function is governed by a variational inequality with gradient constraints. We propose a penalty method to deal with the gradient constraints and then employ the finite difference discretization.
Appears in Collections:Master's Theses (Open)

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