Risk Trading and Endogenous Probabilities in Investment Equilibria
研究了在完全风险市场中，设计者投资风险资产并交易金融证券的均衡问题，发现其可简化为一个随机纳什博弈，其中系统风险代理同时定价风险并决定其他代理使用的概率密度，该概率密度是内生的。
A risky design equilibrium problem is an equilibrium system that involves $N$ designers who invest in risky assets, such as production plants, evaluate these using convex or coherent risk measures, and also trade financial securities in order to manage their risk. Our main finding is that in a complete risk market---when all uncertainties can be replicated by financial products---a risky design equilibrium problem collapses to what we call a risky design game, i.e., a stochastic Nash game in which the original design agents act as risk neutral and there emerges an additional system risk agent. The system risk agent simultaneously prices risk and determines the probability density used by the other agents for their risk neutral evaluations. This situation is stochastic-endogenous: the probability density used by agents to value uncertain investments is endogenous to the risky design equilibrium problem. This result is most striking when design agents use coherent risk measures in which case the intersection of their risk sets turns out to be a risk set for the system risk agent, thereby extending existing results for risk markets. We also investigate existence of equilibria in both the complete and incomplete cases.