Cooperative Hedging in Incomplete Markets

Abstract

The problem of (partial) hedging contingent claims for a single agent is well studied. This paper studies the problem for the multiagent case in incomplete markets. For this case, a cooperative hedging game is posed as follows: First, all agents contribute some money and collect the money together as the initial total capital, then invest the initial 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 the optimal cooperative hedging strategy and prove that the core of the cooperative hedging game, as a cooperative game with side payment, is nonempty.

Key Words:

• Cooperative game
• Core
• Hedging
• Minimax theorem

Mathematics Subject Classification:

• Primary 91B28
• 91A12
• Secondary 60H30

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China under grant 10201031 and the Knowledge Innovation Program of the Chinese Academy of Sciences.