Equilibrium pricing in thin financial markets
In this study, we analyze the equilibrium prices of securities in thin financial markets. We define what a thin market is and focus on the differences to competitive markets. Every agent is characterized by a mean variance utility function and risky endowments, that determine the way she acts in the risk sharing allocation with other agents. The considered market structure that we analyze is a complete one, where agents co-design the securities they trade according to their hedging needs. The allocation and prices of securities are an outcome of a game played by all agents in a form of a pure-strategy Nash equilibrium. We introduce a discrete time dynamic model and dedicate the analysis to bilateral transactions. The results of the so-called re-trading procedure depends on agents for-looking of future rounds. More precisely, behaving myopically or not, results in different outcomes of allocation and prices. In the first case, equilibrium converges to the Pareto optimal risk sharing allocation, while in the latter they stay at an ineffective equilibrium. Also, for some agent, gains may be higher than the optimal allocation of risk sharing. Finally, we examine the case of the evolving course of re-trading, including endogenously given transaction costs for each round.