Are Risk Averse Agents More Optimistic? A Bayesian Estimation Approach

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. This quantity is of particular importance since it characterizes the consensus belief in risk-taking situations with heterogeneous beliefs. Its estimation leads to a nontrivial statistical problem. We start from a large lottery survey (1,536 individuals). We assume that individuals have true unobservable characteristics and that their answers in the survey are noisy realizations of these characteristics. We adopt a Bayesian approach for the statistical analysis of this problem and use an hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We obtain that individuals are on average pessimistic and that pessimism and risk tolerance are positively correlated. As a consequence, we conclude that the consensus belief is biased towards pessimism.Bayesian estimation, MCMC scheme, importance sampling, pessimism, risk tolerance, risk aversion, consensus belief

Are Risk Averse Agents More Optimistic? A Bayesian Estimation Approach

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. This quantity is of particular importance since it characterizes the consensus belief in risk-taking situations with heterogeneous beliefs. Its estimation leads to a nontrivial statistical problem. We start from a large lottery survey (1,536 individuals). We assume that individuals have true unobservable characteristics and that their answers in the survey are noisy realizations of these characteristics. We adopt a Bayesian approach for the statistical analysis of this problem and use an hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We obtain that individuals are on average pessimistic and that pessimism and risk tolerance are positively correlated. As a consequence, we conclude that the consensus belief is biased towards pessimism.Bayesian estimation, MCMC scheme, importance sampling, pessimism, risk tolerance, risk aversion, consensus belief

Are risk averse agents more optimistic? A Bayesian estimation approach

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance.This quantity is of particular importance since it characterizes the consensus belief in risk-taking situations with heterogeneous beliefs. Its estimation leads to a nontrivial statistical problem. We start from a large lottery survey (1536 individuals). We assume that individuals have true unobservable characteristics and that their answers in the survey are noisy realizations of these characteristics. We adopt a Bayesian approach for the statistical analysis of this problem and use an hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We obtain that individuals are on average pessimistic and thatpessimism and risk tolerance are positively correlated. As a consequence, we conclude that theconsensus belief is biased towards pessimism.Bayesian estimation, MCMC scheme, importance sampling, pessimism, risk tolerance, risk aversion, consensus belief.

A comment on Stein's unbiased risk estimate for reduced rank estimators

In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Cand\`es et al. (2013) for singular value soft thresholding, which is a Lipschitz continuous estimator. SURE provides an unbiased risk estimate for an estimator whenever the differentiability requirements for Stein's lemma are satisfied. Lipschitz continuity of the estimator is sufficient, but it is emphasized that differentiability Lebesgue almost everywhere isn't. The reduced rank estimator, which gives the best approximation of the observation with a fixed rank, is an example of a discontinuous estimator for which Stein's lemma actually applies. This was observed by Mukherjee et al. (2015), but the proof was incomplete. This brief note gives a sufficient condition for Stein's lemma to hold for estimators with discontinuities, which is then shown to be fulfilled for a class of spectral function estimators including the reduced rank estimator. Singular value hard thresholding does, however, not satisfy the condition, and Stein's lemma does not apply to this estimator.Comment: 11 pages, 1 figur

Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate- approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure with infinite activity and models in which these small variations are modeled with a Brownian motion. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the choice of the model and we derive an estimation of the model risk

Risk-transfer militarism, small massacres and the historic legitimacy of war

The perception of initial success in the `war against terrorism' appears to strengthen a general relegitimation of war in Western society that has been gathering pace over the last two decades. This article considers the war in Afghanistan as the latest example of the new Western way of war, and analyses its casualties compared with previous campaigns in the Gulf and Kosovo. It identifies the new type as `risk-transfer war', a central feature of which is a `militarism of small massacres'. This new type thus offers only a partial answer to the problems, for the legitimacy of warfare, caused by the systematic targeting of civilians in earlier `degenerate war'. Despite a closer approximation to `just war' criteria, inequalities of risk between Western military personnel and civilians in the zone of war revive the question of legitimacy in a new form. The article suggests that in our concern for relatively small numbers of civilian casualties, we may be applying to war those standards from which it has historically been exempt. In this context the contradictions of the new Western way of war reinforce a `historical pacifist' position towards the legitimacy of warfare

Mechanisms for Risk Averse Agents, Without Loss

Auctions in which agents' payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mechanisms employing internal randomization, partly in response to limitations on deterministic mechanisms imposed by computational complexity. For many of these mechanisms, which are often referred to as truthful-in-expectation, incentive compatibility is contingent on the assumption that agents are risk-neutral. These mechanisms have been criticized on the grounds that this assumption is too strong, because "real" agents are typically risk averse, and moreover their precise attitude towards risk is typically unknown a-priori. In response, researchers in algorithmic mechanism design have sought the design of universally-truthful mechanisms --- mechanisms for which incentive-compatibility makes no assumptions regarding agents' attitudes towards risk. We show that any truthful-in-expectation mechanism can be generically transformed into a mechanism that is incentive compatible even when agents are risk averse, without modifying the mechanism's allocation rule. The transformed mechanism does not require reporting of agents' risk profiles. Equivalently, our result can be stated as follows: Every (randomized) allocation rule that is implementable in dominant strategies when players are risk neutral is also implementable when players are endowed with an arbitrary and unknown concave utility function for money.Comment: Presented at the workshop on risk aversion in algorithmic game theory and mechanism design, held in conjunction with EC 201