![]() " The One-way Fubini Property and Conditional Independence : An Equivalence Result,"Ģ2, Centre for Research in Economic Theory and its Applications CRETA. Journal of Economic Theory, Elsevier, vol. " Perfect competition in asymmetric information economies: compatibility of efficiency and incentives," Sun, Yeneng & Yannelis, Nicholas C., 2007." Monte Carlo Simulation of Macroeconomic Risk with a Continuum of Agents: The Symmetric Case,"Ġ1015, Stanford University, Department of Economics. Applying this analysis to large economies with asymmetric information shows that the con ict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, corresponding to some results in McLean and Postlewaite (2002) and Sun and Yannelis (2007). This leads to a necessary and su cient condition for the classical law of large numbers to hold in a general Hilbert space. In addition to the almost sure convergence of Monte Carlo simulation considered in Hammond and Sun (2008), here we also consider norm convergence when the random variables are square integrable. This paper presents some general properties of such Monte Carlo sampling processes, including their one-way Fubini extension and regular conditional independence. Monte Carlo simulation is used in Hammond and Sun (2008) to characterize a standard stochastic framework involving a continuum of random variables that are conditionally independent given macro shocks.
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