New Results for additive and multiplicative risk apportionment

We provide new characterizations of the preference for additive and multiplicative risk apportionment when risk ordering relies on stochastic dominance. We then point out a simple property of risk apportionment with additive risks: Quite generally, an observed preference for additive risk apportionment in a specific risk environment is preserved when the decision-maker is confronted to other risk situations, so long as the total order of stochastic dominance relationships among risk couples remains the same. The main objective of this paper is to check whether this simple property also holds for multiplicative risks environments. We explain why this is not the case in general, and then provide a set of conditions under which this property holds. We also show that it holds – and even more strongly – in the case of CRRA utility functions due to a particular feature of this family of utility functions.     

Intensity of preferences for bivariate risk apportionment

Bivariate risk apportionment is the preference for dispersing risks associated with two aspects of individuals’ well-being into different states of the world. In this paper, we propose an intensity measure of this preference by extending to the bivariate case the concept of marginal rate of substitution between risks of different orders introduced in the univariate case by Liu and Meyer (2013). We show that the intensity measure of the preference for bivariate risk apportionment is characterized by bivariate risk attitudes in the sense of Ross. The usefulness of our measures to understand economic choices is illustrated by the analysis of two specific decisions: savings under environmental risk and medical treatment in the presence of diagnostic risks.     

Comparative Ross risk aversion in the presence of mean dependent risks

This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessarily mean independent, and may be conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross for mean independent risks. Our theoretical results are related to utility functions having the n-switch independence property.     

Stochastic dominance with pair-wise risk aversion

A class of stochastic orders is defined on the set of bivariate distribution functions. This class of orders is linearly orderable by inclusion. A family of utility functions, coherent with each of the stochastic orders previously defined, is determined. These utility functions represent pair-wise risk aversion. The relations with univariate stochastic orders are examined.     

Ross risk vulnerability for introductions and changes in background risk

We present two theorems that provide necessary and sufficient conditions for an expected utility maximizer to become more risk averse in the sense of Ross with respect to bearing a foreground risk after the introduction of any independent fair or unfair additive background risk. We call these decision makers Ross risk vulnerable, and show that Ross decreasing absolute risk aversion and Ross decreasing absolute prudence are jointly sufficient for Ross risk vulnerability. Restrictions on utility necessary and sufficient for Ross risk vulnerability with respect to stochastic dominance deteriorations of an existing background risk are also presented. Our analysis concludes with applications of Ross risk vulnerability.     

Bayesian identification,selection and estimation of semiparametric functions in high-dimensional additive models

In this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions. Each function is written as a linear combination of basis terms, with coefficients regularized by a proper linearly constrained Gaussian prior. Given any potentially rank deficient prior precision matrix, we show how to derive linear constraints so that the corresponding effect is identified in the additive model. This allows for the use of a wide range of bases and precision matrices in priors for regularization. By introducing indicator variables, each constrained Gaussian prior is augmented with a point mass at zero, thus allowing for function selection. Posterior inference is calculated using Markov chain Monte Carlo and the smoothness in the functions is both the result of shrinkage through the constrained Gaussian prior and model averaging. We show how using non-degenerate priors on the shrinkage parameters enables the application of substantially more computationally efficient sampling schemes than would otherwise be the case. We show the favourable performance of our approach when compared to two contemporary alternative Bayesian methods. To highlight the potential of our approach in high-dimensional settings we apply it to estimate two large seemingly unrelated regression models for intra-day electricity load. Both models feature a variety of different univariate and bivariate functions which require different levels of smoothing, and where component selection is meaningful. Priors for the error disturbance covariances are selected carefully and the empirical results provide a substantive contribution to the electricity load modelling literature in their own right.     

Statistical Disclosure Control Methods for Census Frequency Tables

This paper provides a review of common statistical disclosure control (SDC) methods implemented at statistical agencies for standard tabular outputs containing whole population counts from a census (either enumerated or based on a register). These methods include record swapping on the microdata prior to its tabulation and rounding of entries in the tables after they are produced. The approach for assessing SDC methods is based on a disclosure risk–data utility framework and the need to find a balance between managing disclosure risk while maximizing the amount of information that can be released to users and ensuring high quality outputs. To carry out the analysis, quantitative measures of disclosure risk and data utility are defined and methods compared. Conclusions from the analysis show that record swapping as a sole SDC method leaves high probabilities of disclosure risk. Targeted record swapping lowers the disclosure risk, but there is more distortion of distributions. Small cell adjustments (rounding) give protection to census tables by eliminating small cells but only one set of variables and geographies can be disseminated in order to avoid disclosure by differencing nested tables. Full random rounding offers more protection against disclosure by differencing, but margins are typically rounded separately from the internal cells and tables are not additive. Rounding procedures protect against the perception of disclosure risk compared to record swapping since no small cells appear in the tables. Combining rounding with record swapping raises the level of protection but increases the loss of utility to census tabular outputs. For some statistical analysis, the combination of record swapping and rounding balances to some degree opposing effects that the methods have on the utility of the tables.     

On bivariate generalized binomial and negative binomial distributions

The present paper deals with two types of generalized general binomial (binomial or negative binomial) distributions: (i) a univariate general binomial generalized by a bivariate distribution and (ii) a bivariate general binomial generalized by two independent univariate distributions. The probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials. Moreover recurrence relations for the probabilities and moments, independent of the bipartitional polynomials, are given. Finally these general results are applied to the (i) Binomial-Bivariate Poisson and (ii) Bivariate Binomial-Poissons distributions.     

Differentiability of von Neumann–Morgenstern utility functions

This paper studies necessary and sufficient preference-based conditions for differentiability of risk averse (prudent, or temperate) von Neumann–Morgenstern utility functions. The very idea to devise those conditions is based on the reverse claim of an old observation by Arrow that a risk-averse expected-utility maximizer will always accept a sufficiently small stake in any positive expected-value bet if her von Neumann–Morgenstern utility function is differentiable.     

Rationalizing investors’ choices

Assuming that agents’ preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and of the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.     

信任——风险关系研究的梳理与评价

信任和风险是很多学科研究中的重要问题,两者之间有密切的联系,但对于两者之间到底是什么关系这一问题,学术界存在多个不同的观点。本研究回顾总结了五种代表性观点：风险是信任的结果、风险是信任的前因、风险既是信任的前因又是信任的结果、风险与信任是一种对应关系、风险与信任是一种相互影响关系。文章最后对这些观点给予针对性的评价。     

Is insurance normal or inferior? -A regret theoretical approach-

This study considers how changes in wealth affect insurance demand when individuals suffer disutility from regret. Anticipated regret stems from a comparison between the ex-post maximum and actual wealth. We consider a situation wherein individuals maximize their expected utility incorporating anticipated regret. The wealth effect on insurance demand can be classified into the risk and the regret effects. These effects are determined by the properties of the utility function and the regret function. We show that insurance can be normal when individuals place weight on anticipated regret, even though the utility function exhibit decreasing absolute risk aversion. This result indicates that regret theory is a possible explanation to the wealth effect puzzle, in which insurance is normal from empirical observation, but it should be inferior by theoretical prediction under expected utility theory.     

A new bivariate generalized Poisson distribution

In this paper, a new bivariate generalized Poisson distribution (GPD) that allows any type of correlation is defined and studied. The marginal distributions of the bivariate model are the univariate GPDs. The parameters of the bivariate distribution are estimated by using the moment and maximum likelihood methods. Some test statistics are discussed and one numerical data set is used to illustrate the applications of the bivariate model.     

Analyzing the Relationships between Individual Criminal Behavior and the Severity and Probability of Punishment

This paper deals with problems encountered in analyzing how an individual is deterred from committing a crime by the severity and probability of punishment. It is argued that it might be advantageous to base such an analysis on a model of maximization of expected utility. According to this model, the attractiveness of committing a crime is strongly affected by the product of the relative utility of committing the crime and being punished as compared with the utility of not committing the crime times the probability of the punishment. This implies that the bivariate linear relationships of choices to commit or not to commit crime and the severity and probability factors are dependent on the variations in both these factors and their mean values. In this paper, these bivariate relationships are analyzed in two ways – formally-algebraically and by numerical examples.     

高阶矩风险与金融投资决策

针对传统投资组合理论没有考虑高阶矩风险这一缺陷,总结近期金融领域中有关偏度和峰度的研究成果,基于"均值-方差"效用函数的Taylor展开,讨论了投资者对高阶矩风险(偏度风险和峰度风险)的偏好特征。     

Extrapolation‐based Bandwidth Selectors: A Review and Comparative Study with Discussion on Bivariate Applications

Cross‐validation is a widely used tool in selecting the smoothing parameter in a non‐parametric procedure. However, it suffers from large sampling variation and tends to overfit the data set. Many attempts have been made to reduce the variance of cross‐validation. This paper focuses on two recent proposals of extrapolation‐based cross‐validation bandwidth selectors: indirect cross‐validation and subsampling‐extrapolation technique. In univariate case, we notice that using a fixed value parameter surrogate for indirect cross‐validation works poorly when the true density is hard to estimate, while the subsampling‐extrapolation technique is more robust to non‐normality. We investigate whether a hybrid bandwidth selector could benefit from the advantages of both approaches and compare the performance of different extrapolation‐based bandwidth selectors through simulation studies, real data analyses and large sample theory. A discussion on their extension to bivariate case is also presented.     

Forecasting expected shortfall: Should we use a multivariate model for stock market factors?

Is univariate or multivariate modeling more effective when forecasting the market risk of stock portfolios? We examine this question in the context of forecasting the one-week-ahead expected shortfall of a stock portfolio based on its exposure to the Fama–French and momentum factors. Applying extensive tests and comparisons, we find that in most cases there are no statistically significant differences between the forecasting accuracy of the two approaches. This result suggests that univariate models, which are more parsimonious and simpler to implement than multivariate factor-based models, can be used to forecast the downside risk of equity portfolios without losses in precision.     

效用理论在飞行安全风险评估中的应用

为科学划分飞行安全风险等级,将效用理论引入飞行安全风险领域,利用效用函数,建立了飞行安全风险评估模型。在分析飞行安全风险的基础上,通过定义事故或危险事件损失效应,选取合适的效用函数进行飞行安全风险的度量。模型有效区分了类似飞行事故这样高损失、低概率事件与飞行事故征候这样低损失、高概率事件风险之间的差异,克服了期望值法的局限性。最后通过实例验证了该方法的科学性和有效性。     

Implicitly additive utility and the nature of optimal economic growth

The solution of an optimization problem frequently depends only on the constraint set and on the indifference set through the optimum. This observation is spelled out and applied to the problem of optimal economic growth. The validity of the turnpike property of optimal growth plans is investigated when the intertemporal utility function is not additive, but has the property that each of its indifference sets is also an indifference set for some other utility function which is additive and has a constant rate of discount. A characterization is provided for such utility functions, which are called implicitly additive.     

Risk aversion for variational and multiple-prior preferences

The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents’ choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.