Dynamic Cooperative Investment

In this thesis we develop dynamic cooperative investment schemes in discrete and continuous time. Instead of investing individually, several agents may invest joint capital into a commonly agreed trading strategy, and then split the uncertain outcome of the investment according to the pre-agreed scheme, based on their individual risk-reward preferences. As a result of cooperation, each investor is able to get a share, which cannot be replicated with the available market instruments, and because of this, cooperative investment is usually strictly profitable for all participants, when compared with an optimal individual strategy. We describe cooperative investment strategies which are Pareto optimal, and then propose a method to choose the most ‘fair’ Pareto optimal strategy based on equilibrium theory. In some cases, uniqueness and stability for the equilibrium are justified. We study a cooperative investment problem, for investors with different risk preferences, coming from expected utility theory, mean-variance theory, mean-deviation theory, prospect theory, etc. The developed strategies are time-consistent; that is the group of investors have no reasons to change their mind in the middle of the investment process. This is ensured by either using a dynamic programming approach, by applying the utility model based on the compound independence axiom. For numerical experiments, we use a scenario generation algorithm and stochastic programming model for generating appropriate scenario tree components of the S&P 100 index. The algorithm uses historical data simulation as well as a GARCH model.