Multi-agent investment in incomplete markets

The problem of the expected utility maximization in incomplete markets for a single agent is well understood in a fairly general setting. This paper studies the problem for the multi-agent case. For this case a cooperative investment game is posed as follows: firstly collect all agents capital together at the initial time, then invest the total capital in a trading strategy, and finally divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of Pareto optimal cooperative strategies and a characterization of situations where cooperation strictly Pareto dominates non cooperation, and prove that the core of the cooperative investment game is non-empty under mild conditions using Scarf theorem.Received: August 2003, Mathematics Subject Classification (1991): 91B28, 91A12, 60H30JEL Classification: G11, C71This work is supported by the National Natural Science Foundation of China under grant 10201031. It is a pleasure for the author to express his sincere thanks to an anonymous referee for valuable suggestions.