This thesis is concerned with the modelling and algorithmic development of a Stopping Rule Problem (SRP) in the area of Portfolio Management. More specifically, the objective is to provide an exit strategy for an invested portfolio containing one or more assets. The exit strategy aims to protect gains in addition to limiting losses. The thesis focuses on the investment/disinvestment in the portfolio and is not concerned with the composition of the portfolio.

A new Finite Horizon SRP, referred to as the Portfolio Management Problem (PMP), has been proposed that allows future scenarios to be considered in the optimisation of the exit time. The PMP aims at maximizing the expected reward of a Portfolio Manager (PM) through an optimal policy. A Dynamic Programming approach is proposed and the DP algorithm developed is capable of solving real-life problems for short- and long-term trades.

The applicability of the PMP is limited to cases where no constraints have been imposed by the PM. In view of adding more realism into the model, a Stop Loss and Target Return has been encapsulated in the formulation of the PMP model and thus, in the optimisation of the exit time. The impact of the model with enhanced managerial capabilities, is a better control of the maximum drawdown which restricts the risk of investment, influencing positively metrics of performance. An efficient tradeoff between computational time and size of problem solved has been developed.

The final part of this thesis focuses on a PMP which takes into consideration in a dynamic way the new market information for the determination of the optimal policy for assets exhibiting Mean-reversion (MR). This has been achieved through the insertion of a MR Rule specifically developed for the PMP which quantifies future tendencies of the asset prices based on its varying average. An algorithm dealing with the further additional memory requirements has been developed, capable of solving problems of size identical to the original PMP.