Synergy effect of cooperative investment

Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents’ preferences are represented by mean-deviation functionals, sharing of optimal portfolio creates instruments that, on the one hand, satisfy individual risk preferences but, on the other hand, are not replicable on an incomplete market, so that each agent is strictly better off in participating in cooperative investment than investing alone. This synergy effect is shown to hold when agents’ acceptance sets are represented by cash-invariant utility functions in the case of multiperiod investment with an arbitrary feasible investment set. In this case, a set of all Pareto-optimal allocations is characterized, and an equilibrium-based method for selecting a “fair” Pareto-optimal allocation is suggested. It is also shown that if exists, the “fair” allocation belongs to the core of the corresponding cooperative game. The equilibrium-based method is then extended to the case of arbitrary utility functions. The obtained results are demonstrated in a multiperiod cooperative investment problem with investors imposing drawdown constraints on investment strategies.