Xu, Junwei
(2017)
Topics in optimal liquidation and contract theory.
PhD thesis, London School of Economics and Political Science.
Abstract
The thesis consists of three parts. The first one presents an exhaustive study of three new models arising in the context of the so-called optimal liquidation problem. This is the problem faced by an investor who aims at selling a large number of stock shares within a given time horizon and wants to maximise his expected utility of the cash resulting from the sale. Such an investor has to take into account the impact that his selling strategy has on the underlying stock price. The models studied in the thesis assume that market risk follows a fairly general L´evy process and that the investor has an exponential utility. In each of the three different model formulations, an explicit or semi-explicit expression for the optimal liquidation strategy is derived.
The second part of the thesis presents a study of an optimal liquidation problem embedded in a contractual problem. In particular, a contractual relationship between an investor and a broker is modelled on the basis of a suitable liquidation strategy and the corresponding affected mark-to-market assert price. The analysis of the model determines the broker’s compensation and the liquidation strategy that maximise the broker’s as well as the investor’s expected utilities.
The third part of the thesis studies a continuous time principal-agent problem in which the agent’s outside options depend on his past performance. In this new model, even if the agent does not expect any compensation from the principal at all, the agent may still apply work effort with a view to improving his outside options. Formulated as an optimal control and stopping problem for both the agent and the principal, the optimal contract is identified.
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