A pair of explicitly solvable impulse control problems.

AlAzemi, Fares M.M.S (2010) A pair of explicitly solvable impulse control problems. PhD thesis, London School of Economics and Political Science.

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Abstract

This thesis is concerned with the formulation and the explicit solution of two impulse stochastic control problems that are motivated by applications in the area of sequential investment decisions. Each of the two problems considers a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Ito diffusion. In the first of the two problems, the control that can be applied to the system takes the form of one-sided impulsive action, and the associated objective is to maximise a performance criterion that rewards high values of the utility derived from the system's controlled state and penalises the expenditure of any control effort. Potential applications of this model arise in the area of real options where one has to balance the sunk costs incurred by investment against their resulting uncertain cashflows. The second model is concerned with the so-called buy-low and sell-high investment strategies. In this context, an investor aims at maximising the expected discounted cash-flow that can be generated by sequentially buying and selling one share of a given asset at fixed transaction costs. Both of the control problems are solved in a closed analytic form and the associated optimal control strategies are completely characterised. The main results are illustrated by means of special cases that arise when the uncontrolled system dynamics are a geometric Brownian motion or a mean-reverting square-root process such as the one in the Cox-Ingersoll-Ross interest rate model.

Item Type:	Thesis (PhD)
Uncontrolled Keywords:	Mathematics
Sets:	Collections > ProQuest Etheses Departments > Mathematics
URI:	http://etheses.lse.ac.uk/id/eprint/2773

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