We consider a market of a given vector of securities and finitely many financial agents, who are heterogeneous with respect to their risky endowments and risk aversions. The market is assumed to be thin, meaning that each agent's actions could heavily influence the price and allocation of the securities. We propose a market model where agents strategically choose the risk aversion that they will implement in the trading. In this environment, equilibrium is modelled as the outcome of a Nash-type game (in the spirit of Kyle, 1989), where the agents' sets of strategic choices are the demand functions on the tradeable securities.

Under standard assumptions, we first show that the agents have motive to declare different risk aversions than their true ones, and in particular, when the correlation between an agent's endowment and the market risk is low (resp. high), the agent tends to behave in a more (resp. less) risk averse manner. The Nash equilibrium is then characterized as a solution to a system of quadratic equations, which is shown to have a unique solution under some mild additional assumptions.

Interestingly enough, it is shown that agents with higher exposure to market risk and/or sufficiently low (true) risk aversion profit more from the Nash equilibrium as compared to the Arrow-Debreu one (i.e., with no strategic behavior). Finally, we connect the findings of this work to similar results provided in recently established models where agents strategically choose their reported beliefs and their submitted risk exposures.

This is joint work with C. Kardaras (LSE) and G. Vichos (LSE).

Speaker(s): Michalis Anthropelos (University of Piraeus)