An axiomatic analysis of economic equilibrium, new haven. Pdf a path to the arrowdebreu competitive market equilibrium. His research focuses on quantitative behavioral finance models that incorporate human emptions and psychology into financial decision making, and on intelligent wealth management solutions using optimal control and machine learning techniques. Asset price bubbles in arrowdebreu and sequential equilibrium. Zhou, arrow debreu equilibria for rank dependent utilities, mathe. Garg and kapoor 2004 gave some very interesting approximate equilibrium algorithms for the linear case of both models using an auction based approach. The ces constant elasticity of substitution utility functions have drawn much attention. In fact, our proof shows that this market equilibrium problem does not have a fully polynomialtime approximation scheme unless every problem in ppad is solvable in polynomial time. Can anyone also explain the criteria required for the model to have a unique equilibrium.
Net by olav bjerkholt, department of economics, university of oslo. Moreover, probability distortion tends to increase the price of insurance increase asset returns. In fact, our proof shows that this marketequilibrium problem does not have a fully polynomialtime approximation scheme unless every problem in ppad is solvable in polynomial time. While the cases of rank dependence and ambiguity are formally similar, an important distinction emerges as for rank dependent preferences equilibria are determinate, while for ambiguity they are generally indeterminate.
Arrow, debreu, mckenzie and the problem of scientific credit. Results without real analyticity in the space variables b. Program of the workshop in quantitative behavioural finance with schedule and download of the schedule. A trade application of the arrow debreu leontief equilibrium.
All investors are risk averse expected utility maximizers. Computational economy equilibrium and its application. Arrowdebreu model of general equilibrium springerlink. A basic arrowdebreu security for state s pays its owner 1 unit of output on date 2 if state s occurs and nothing otherwise. Arrowdebreu equilibria for rankdependent utilities with heterogeneous probability weighting jin, h. Arrow debreu equilibria for rank dependent utilities with heterogeneous probability weighting hanqing jin jianming xiay xun yu zhouz august 8, 2018 abstract we study arrow debreu equilibria for a oneperiodtwodate pure exchange economy with rank dependent utility agents having heterogeneous probability weighting and outcome utility functions. N2 price bubbles in an arrow debreu equilibrium in an infinitetime economy are a manifestation of lack of countable additivity of valuation of assets. Moreover, although delivery is contingent upon the state of nature that is revealed, payment is not. Arrowdebreuequilibriaforrankdependent utilities portfoliochoiceunderrdut quantileformulation quantile formulation. A combinatorial polynomial algorithm for the linear arrow. Define a pareto efficient allocation for this economy. A path to the arrowdebreu competitive market equilibrium 5 where the given a is an m. Market equilibrium under piecewise leontief concave utilities. Apr 07, 2009 hardness of finding equilibria in arrow debreu markets april 7, 2009 by algorithmicgametheory a paper titled settling the complexity of arrow debreu equilibria in markets with additively separable utilities by xi chen, decheng dai, ye du, and shanghua teng was recently posted to the arxiv.
Huang and jan werner december 2002 rwp 0208 research division federal reserve bank of kansas city kevin x. Jianming xia xun yu zhou august 12, 2016 abstract westudyarrowdebreuequilibriaforaoneperiodtwodatepureexchange economy with rank dependent utility agents having heterogeneous probability weighting and outcome utility functions. The classical arrow debreu theorem is described, for example, in k. Prof xunyu zhou from the chinese university of hong kong and university of oxford provides conditions on a oneperiodtwodate pure exchange economy with rank dependent utility agents under which arrow debreu equilibria exist, and describes the findings based on the result. Characterization and uniqueness of equilibrium, siam journal on control and op timization, vol. Existence of an equilibrium for a competitive economy. Arrow debreu equilibria for rankdependent utilities. Arrowdebreu equilibria for rankdependent utilities, mathematical finance, wiley blackwell, vol.
Calculate a pareto efficient allocation by maximizing a weighted sum of utilities. The model economy for which the theorem could be proved was mapped out in 1954 by kenneth arrow and gerard debreu collaboratively, and by lionel mckenzie separately, and would become widely known as the arrow debreu model. Arrowdebreu equilibria for rankdependent utilities with. Devanur and vazirani 2004 extended spending constraint utilities to the arrowdebreu model and established many nice properties of these utilities. Arrowdebreu equilibria for rankdependent utilities with heterogeneous probability weighting hanqing jin. Financial market equilibria with cumulative prospect theory. Arrow debreu equilibria for rank dependent utilities with heterogeneous probability weighting hanqing jin. On page 6, is shown in figure 4 how the model is set up. Arrowdebreu equilibrium for rankdependent utility with. Hardness of finding equilibria in arrowdebreu markets. Settling the complexity of arrowdebreu equilibria in markets. This is a simple corollary of the preceding proposition. Arrowdebreu model of general equilibrium having many.
Dilip mookherjee ec703 problem set 6, with solutions 1. We prove that the problem of computing an arrow debreu market equilibrium is ppadcomplete even when all traders use additively separable, piecewiselinear and concave utility functions. When such an equilibrium exists, we derive the stateprice density explicitly, which is a weighted marginal. The arrowdebreu model of general competitive equilibrium in. Classes of arrow debreu leontief equilibrium problems solvable in strongly polynomial time, polynomial time, or fptas. Arrows result can be easily extended to a multidate economy with. Jianming xia, xun yu zhou article first published online. Arrow debreu equilibria for rank dependent utilities. In particular, we allow the economy to have a mix of expected utility agents and rankdependent utility ones, with nonconvex probability weighting functions. Sep 01, 2009 the classical arrowdebreu theorem is described, for example, in k. Arrowdebreu model of general equilibrium having many equilibria. We study arrow debreu equilibria for a oneperiodtwodate pure exchange economy with rankdependent utility agents having heterogeneous probability weighting and outcome utility functions.
Equilibrium asset pricing with epsteinzin and lossaverse investors, journal of economic dynamics and control, elsevier, vol. Competitive equilibria in a comonotone market 251 table of contents introduction competitive equilibria with dual utilities competitive equilibria with rank dependent utilities an algorithm for computing competitive equilibria conclusion based on joint work with tim boonen amsterdam and fangda liu cufe, beijing 2 51. Consider the exchange economy described in that problem. Agents utility in the absence of trade statecontingent utility expected utility in period 1. Jianming xia xun yu zhou august 12, 2016 abstract westudyarrow debreuequilibriaforaoneperiodtwodatepureexchange economy with rankdependent utility agents having heterogeneous probability weighting and outcome utility functions. Arrow debreu equilibria for rank dependent utilities xunyu zhou the university of oxford, uk we provide conditions on a pure exchange economy with rank dependent utility agents under which arrow debreu equilibria exist. Arrow debreu equilibria for rankdependent utilities article in mathematical finance 263 september 2012 with 36 reads how we measure reads.
In this paper we study implementation of arrowdebreu equilibrium allocations. Mathematical finance arrow debreu equilibria for rank. We provide conditions on a pure exchange economy with rank dependent utility agents under which arrow debreu equilibria exist. Time polynomial arrowdebreu market equilibrium microsoft. Arrowdebreu, 1954, two of the oldest and most important questions of neoclassical economics, the viability and efficiency of the market system, were shown to be susceptible to analysis in a model completely faithful to the neoclassical methodological premises of individual. Xia, jianming and zhou, xunyu, arrow debreu equilibria for rank. Arrowdebreu equilibria for rankdependent utilities by. Market equilibrium is a fundamental solution concept in mathematical economics and has been studied extensively since the work of walras. Computational market equilibrium yinyu ye, wine2008 2 outlines the arrow debreu competitive equilibrium problem. Arrowdebreu equilibria for rankdependent utilities. Lastly, we show that in some restricted settings, some results may be used to prove uniqueness of arrowradner equilibria when there are incomplete financial markets. In contrast, a riskless bond pays its owner the same amount of output in every state. Arrowdebreu competitive market equilibrium problems with linear utilities and n players. 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.
Problem set 7, with solutions bu personal websites. Arrow debreu vs capm the arrow debreu framework was developed in the 1950s and 1960s by kenneth arrow us, b. A path to the arrowdebreu competitive market equilibrium. Problem set 6, with solutions bu personal websites. When such an equilibrium exists, we show that the state. The notion of equilibrium is inherently algorithmic, with many applications in policy analysis and recently in ecommerce. In particular, we allow the economy to have a mix of expected utility agents and rank. Allowing agents to care about their own consumption and the distribution of consumption possibilities in the economy, the competitive equilibria are efficient given prices if and only if there is.
When the expected utilities are distorted by probability weighting functions, players cannot find explicit optimal decisions. An arrow debreu economy general equilibrium supply demand with production if desired static but multiperiod. Financial market equilibria with cumulative prospect theory article in journal of mathematical economics 465. Read table of contents, mathematical finance on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. In fact, our proof shows that this marketequilibrium problem does not have a fully polynomialtime approximation scheme unless every problem in ppad. While arrow and debreu would later go on to win separate nobel prizes in economics, mckenzie would never receive it. Settling the complexity of arrowdebreu equilibria in. For this exposition, we restrict ourself to a single consumption good only. General arrowdebreu equilibrium can be determined for expected utility maximisers by explicit solutions for individual players. Debreu, existence of an equilibrium for a competitive economy econometrica, 22. Arrowdebreu equilibria for rankdependent utilities with heterogeneous probability weighting. The dual theory of choice under risk, econometrica, econometric society, vol. Find the transfer payments necessary to implement the pareto efficient allocation in part b as an equilibrium with transfers. Continuoustime asset pricing, dynamic market completeness, general equilibrium theory.
An arrow debreu exchange market consists of a set of agents and a set of divisible goods. Xunyu zhou is the liu family professor of financial engineering at columbia university in new york. Arrowdebreu equilibrium prices this section explains arrow debreuprices in an equilibrium context, where they originated, see arrow 1953 and debreu 1959. There are also algorithms for the arrowdebreu model with nonlinear utilities.
Implementing arrowdebreu equilibria by trading infinitelylived securities kevin x. We provide conditions on a oneperiodtwodate pure exchange economy with rank dependent utility agents under which arrow debreu equilibria exist. Optimal insurance under rankdependent expected utility. Xunyu zhou industrial engineering and operations research. N, we let xi 0 x i 0 and x xi play the roles of z 0 and z in the proposition. Since the returns of the two assets are linearly independent rank of the return matrix is 2, the set of radner equilibria of this economy is the same as the set of equilibria of an arrow securities economy, which in turn is the same as the set of arrow debreu equilibria.