Pricing Risk Under Risk Measures: An Introduction to Stochastic-Endogenous Equilibria
45 Pages Posted: 4 Aug 2011
Date Written: August 2, 2011
Abstract
We investigate risk averse agents who manage risk by trading financial securities in a market that we call a risk market. We assume this market is perfectly competitive and complete. When risk aversion is expressed using risk measures, the (bundle of) prices for financial securities turns out to be a probability density function, PDF. This endogeneity of probability distributions defines a novel template for equilibria under uncertainty and, more specifically, equilibria under risk. It is particularly striking that when agents use coherent risk measures to assess uncertain outcomes, a most risk neutral agent emerges from the risk market: its risk set is precisely the intersection of all agents’ risk sets, and the endogenous price of risk is simultaneously a worst case PDF for the most risk neutral agent and for each agent individually. We also show that risk markets can be conveniently adapted to decision making models like Nash games under risk, where agents are risk averse and optimize their actions under uncertainty.
Keywords: Risk aversion, coherent risk measure, risk set, risk trading, most risk neutral, least risk averse, equilibria under risk, games under risk, stochastic-endogenous equilibrium, complete market, perfect competition
JEL Classification: C62, C73, D41, D81, E22, G12, G13
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Beyond Arbitrage: 'Good Deal' Asset Price Bounds in Incomplete Markets
-
Beyond Arbitrage: "Good-Deal" Asset Price Bounds in Incomplete Markets
-
Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities
By Jun Liu and Francis A. Longstaff
-
By James Dow and Gary B. Gorton
-
Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets
By Aleš Černý
-
The Theory of Good-Deal Pricing in Financial Markets
By Aleš Černý and Stewart D. Hodges
-
Imperfect Arbitrage with Wealth Effects
By Wei Xiong
-
Towards a General Theory of Good Deal Bounds
By Tomas Bjork and Irina Slinko