111 research outputs found
Robust Optimal Risk Sharing and Risk Premia in Expanding Pools
We consider the problem of optimal risk sharing in a pool of cooperative
agents. We analyze the asymptotic behavior of the certainty equivalents and
risk premia associated with the Pareto optimal risk sharing contract as the
pool expands. We first study this problem under expected utility preferences
with an objectively or subjectively given probabilistic model. Next, we develop
a robust approach by explicitly taking uncertainty about the probabilistic
model (ambiguity) into account. The resulting robust certainty equivalents and
risk premia compound risk and ambiguity aversion. We provide explicit results
on their limits and rates of convergence, induced by Pareto optimal risk
sharing in expanding pools
Entropy coherent and entropy convex measures of risk
We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized version, respectively, of) the popular maxmin expected utility theory of Gilboa and Schmeidler [12] whenever the negative certainty equivalents are translation invariant. In addition, we derive the dual conjugate function for entropy coherent and entropy convex measures of risk, and prove their distribution invariant representation. Keywords: Robust preferences; Convex risk measures; Exponential utility; Relative entropy; Translation invariance; Convexity
Asymptotically distribution-free goodness-of-fit testing for tail copulas
Let be an i.i.d. sample from a bivariate
distribution function that lies in the max-domain of attraction of an extreme
value distribution. The asymptotic joint distribution of the standardized
component-wise maxima and is then
characterized by the marginal extreme value indices and the tail copula . We
propose a procedure for constructing asymptotically distribution-free
goodness-of-fit tests for the tail copula . The procedure is based on a
transformation of a suitable empirical process derived from a semi-parametric
estimator of . The transformed empirical process converges weakly to a
standard Wiener process, paving the way for a multitude of asymptotically
distribution-free goodness-of-fit tests. We also extend our results to the
-variate () case. In a simulation study we show that the limit theorems
provide good approximations for finite samples and that tests based on the
transformed empirical process have high power.Comment: Published at http://dx.doi.org/10.1214/14-AOS1304 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Expected utility and catastrophic risk in a stochastic economy-climate model
We analyze a stochastic dynamic finite-horizon economic model with climate change, in which the social planner faces uncertainty about future climate change and its economic damages. Our model (SDICE*) incorporates, possibly heavy-tailed, stochasticity in Nordhaus’ deterministic DICE model. We develop a regression-based numerical method for solving a general class of dynamic finite-horizon economy–climate models with potentially heavy-tailed uncertainty and general utility functions. We then apply this method to SDICE* and examine the effects of light- and heavy-tailed uncertainty. The results indicate that the effects can be substantial, depending on the nature and extent of the uncertainty and the social planner's preferences
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