The Effect of Market Power on Risk-Sharing

Abstract

Abstract. The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent's set of strategic choices consists of the security payoffs and the pricing kernel that are consistent with the optimal-sharing rules; while in the incomplete setting, agents respond via demand functions on a vector of given tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium, the sharing securities are suboptimal, since agents submit for sharing different risk exposures than their true endowments. On the other hand, the Nash equilibrium prices stay unaffected by the game only in the special case of agents with the same risk aversion. In addition, agents with sufficiently lower risk aversion act as predatory traders, since they absorb utility surplus from the high risk averse agents and reduce the efficiency of sharing. The main results of the paper also hold under the generalized models that allow the presence of noise traders and heterogeneity in agents' beliefs.

Equilibrium returns with transaction costs

“…In the present quadratic context, this result holds true exactly. A result in the same spirit in a static model is [4,Corollary 4.12], where incompleteness also only affects strategies but not equilibrium prices for mean-variance investors with homogenous risk aversions. Another related result is [38,Proposition 12], where homogeneous risk aversion imply that the frictional equilibrium converges to the frictionless one as the horizon grows.…”

“…Since our goal is to obtain a model with maximal tractability, it is natural to assume that the exogenous volatility matrix σ is constant. 4 However, stochastic volatilities are bound to appear naturally in more general models where they are determined endogenously. Such extensions of the current setting are an important direction for further research.…”

“…This will be the time-discount rate below; for infinite horizon models, it needs to be strictly positive 4. If one instead assumes that the volatility follows some (sufficiently integrable) stochastic process (σt) t∈T , then the subsequent characterization of individually optimal strategies and equilibrium returns in terms of coupled but linear FBSDEs as in (A.1)-(A.2) still applies.…”