

International conference "Stochastic Optimization and Optimal Stopping"
September 25, 2012 10:00–10:50, Moscow, Steklov Mathematical Institute of RAS





Plenary talks


ArrowDebreu equilibria for rankdependent utilities
Xunyu Zhou^{} ^{} Chinese University of Hong Kong

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Abstract:
We provide conditions on a pure exchange economy with rankdependent utility agents under which ArrowDebreu equilibria exist. When such an equilibrium exists, we derive the stateprice density explicitly, which is a weighted marginal rate of substitution between initial and endofperiod consumption of a representative agent, while the weight is expressed through the differential of the probability weighting function. A key step in our derivation is to obtain an analytical solution to the individual consumption optimization problem that involves the concave envelope of certain nonconcave function. Based on the result we have several findings, including that asset prices depend upon agents' subjective belief on overall consumption growth, that an uncorrelated security's entire probability distribution and its dependence with the other part of the economy should be priced, and that there is a direction of thinking about the equity premium puzzle and the riskfree rate puzzle. Moreover, we propose a “rankneutral probability” that is an appropriate modification of the original probability
measure under which assets can be priced in the same way as in an economy with expected utility agents. This is a joint work with Jiangming Xia.
Language: English

