The Optimal Timing of Investment Decisions

This thesis addresses the problem of the optimal timing of investment decisions. A number of models are formulated and studied. In these, an investor can enter an investment that pays a dividend, and has the possibility to leave the investment, either receiving or paying a fee. The objective is to maximise the expected dis-counted cashflow resulting from the investor’s decision making over an infinite time horizon. The initialisation and abandonment costs, the discounting factor, and the running payoffs are all functions of a state process that is modelled by a general one-dimensional positive Ito ̂ diffusion. Sets of sufficient conditions that lead to results of an explicit analytic nature are identified. These models have numerous applications in finance and economics. To address the family of models that we study, we first solve the discretionary stopping problem that aims at maximising the performance criterion Ex e− R τ 0 r(Xs)dsg(Xτ)1{τ<∞} over all stopping times τ, whereX is a general one-dimensional positive Ito ̂ diffusion, r is a strictly positive function and g is a given payoff function. Our analysis, which leads to results of an explicit analytic nature, is illustrated by a number of special cases that are of interest in applications, and aspects of which have been considered in the literature and we establish a range of results that can provide useful tools for developing the solution to other stochastic control problems