Profit criteria involving risk in price setting of virtual products

This work deals with pricing of “virtual” products, i.e., products that a retailer can supply after demand has been realized. Such products allow the retailer to avoid holding costs and ensure timely fulfillment of demand with no risk of shortage. Demand is commonly price-dependent and uncertain, and we seek to maximize each of three criteria: expected profit, the likelihood of achieving a profit target, and the profit for a given percentile. Simultaneous multiple criteria are also explored. Two forms of demand uncertainty are considered in the analysis: the multiplicative form, where, due to stochastic dominance, all the investigated profit criteria—and, in fact, any utility function of the profit—can be optimized simultaneously; and the additive form, where stochastic dominance cannot occur. Under the multiplicative form of demand, the property of stochastic dominance is shown to hold in a two-echelon supply chain (comprising both the supplier and the retailer) and in a centralized system.     

区间二型模糊集效用函数和熵在风险决策中的应用

针对以区间二型模糊集(IT2FS)为信息环境的多属性决策(MADM)问题,引入IT2FS效用函数,并提出基于IT2FS效用函数,熵和风险因子的风险决策模型。首先基于截集思想提出两种IT2FS效用函数公式,有效提取了IT2FS全部信息,比以往的序值型公式更加科学有效。其次基于已提出的IT2FS三种不确定度量存在的问题提出三种新型不确定度量,并基于此三种不确定度量提出IT2FS熵公式弥补原有熵度量的不足。再次引入风险偏好因子反映决策者不同的风险态度,并改进风险偏好因子范围。构造基于效用函数,熵和风险偏好因子的风险决策模型。最后利用一个实例分析结果表明,该风险决策模型中决策者风险偏好对属性权重以及方案的排序存在影响,该决策思想对风险投资决策和风险管理决策均有一定的参考作用。     

Representing risk preferences in expected utility based decision models

Users of expected utility based decision models frequently find it useful or necessary to specify a functional form that represents the risk preferences of a decision maker. Having additional functional forms from which to choose would be helpful. The literature so far has provided several such functional forms for the utility function itself. The discussion presented here indicates that providing a functional form for the marginal utility function is an alternate and equally useful way to represent risk preferences. Furthermore, functional forms for marginal utility are easier to provide, and there exist functional forms for marginal utility that represent simple risk preferences for which there is no associated functional form for the utility function. Several functional forms for marginal utility are suggested, and the class of isoelastic risk preferences is identified and discussed.     

基于中国地震的损失模型(英文)

对损失分布的估计一直是保险公司的重要问题. 有多种参数方法以及非参数方法拟合损失分布. 本文作者提出了结合参数和非参数的方法来解决损失分布拟合问题. 首先通过超额均值图确定大小损失之间的阈限,再利用广义Pareto分布拟合阈值以上损失, 转换后的核密度估计拟合阈值以下损失. 最后, 通过实证分析将该方法和其他方法进行了误差分析比较, 取得了理想的结果.     

Nonparametric conditional autoregressive expectile model via neural network with applications to estimating financial risk

The parametric conditional autoregressive expectiles (CARE) models have been developed to estimate expectiles, which can be used to assess value at risk and expected shortfall. The challenge lies in parametric CARE modeling is the specification of a parametric form. To avoid any model misspecification, we propose a nonparametric CARE model via neural network. The nonparametric CARE model can be estimated by a classical gradient based nonlinear optimization algorithm, and the consistency of nonparametric conditional expectile estimators is established. We then apply the nonparametric CARE model to estimating value at risk and expected shortfall of six stock indices. Empirical results for the new model is competitive with those classical models and parametric CARE models. Copyright © 2016 John Wiley & Sons, Ltd.     

Household risk aversion and portfolio choices

In practice, stock investment is one of the most important decisions made by households. The primary goal of this paper is to explain family investment decisions under the assumptions of household member’s preferences and efficient risk sharing based on the collective household model. In particular, by examining the absolute (relative) risk aversion of the household welfare function, we demonstrate how household’s portfolio allocation in stocks changes with family wealth. We examine two types of preference heterogeneity between family members: parameter heterogeneity and functional form heterogeneity. This study offers an alternative explanation of household portfolio choice corresponding with the observation that wealthier households tend to hold greater share of their wealth in risky assets. Specifically, if two decision-makers have standard constant relative risk aversion preference with different relative risk aversions in a household, family’s relative risk aversion decreases as household wealth increases (decreasing relative risk aversion).     

A decision theory for partially consonant belief functions

Partially consonant belief functions (pcb), studied by Walley, are the only class of Dempster-Shafer belief functions that are consistent with the likelihood principle of statistics. Structurally, the set of foci of a pcb is partitioned into non-overlapping groups and within each group, foci are nested. The pcb class includes both probability function and Zadeh’s possibility function as special cases. This paper studies decision making under uncertainty described by pcb. We prove a representation theorem for preference relation over pcb lotteries to satisfy an axiomatic system that is similar in spirit to von Neumann and Morgenstern’s axioms of the linear utility theory. The closed-form expression of utility of a pcb lottery is a combination of linear utility for probabilistic lottery and two-component (binary) utility for possibilistic lottery. In our model, the uncertainty information, risk attitude and ambiguity attitude are separately represented. A tractable technique to extract ambiguity attitude from a decision maker behavior is also discussed.     

Event risk, contingent claims and the temporal resolution of uncertainty

We study the pricing and hedging of contingent claims that are subject to Event Risk which we define as rare and unpredictable events whose occurrence may be correlated to, but cannot be hedged perfectly with standard marketed instruments. The super-replication costs of such event sensitive contingent claims (ESCC), in general, provide little guidance for the pricing of these claims. Instead, we study utility based prices under two scenarios of resolution of uncertainty for event risk: when the event is continuously monitored, or when it is revealed only at the payment date. In both cases, we transform the incomplete market optimal portfolio choice problem of an agent endowed with an ESCC into a complete market problem with a state and possibly path-dependent utility function. For negative exponential utility, we obtain an explicit representation of the utility based prices under both information resolution scenarios and this in turn leads us to a simple characterization of the early resolution premium. For constant relative risk aversion utility functions we propose a simple numerical scheme and study the impact of size of the position, wealth and expected return on these prices.     

Econometric modeling of risk measures: A selective review of the recent literature

Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review,the concentration is on recent developments in the estimation of the most popular risk measures,namely, value at risk(VaR), expected shortfall(ES), and expectile. After introducing the concept of risk measures, the focus is on discussion and comparison of their econometric modeling.Then, parametric and nonparametric estimations of tail dependence are investigated. Finally,we conclude with insights into future research directions.     

Utility Representations of Preferences on General Choice Spaces

The purpose of this paper is to reconsider the utility representation problem of preferences. Several representation theorems are obtained on general choice spaces. Preferences having continuous utility functions are characterized by their continuities and countable satiation. It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a continuous utility function is that the preference is continuous and countably satiable. For monotone preferences,we obtain that any space has continuous utility representations.     

Nonparametric variable selection and its application to additive models

Variable selection for multivariate nonparametric regression models usually involves parameterized approximation for nonparametric functions in the objective function. However, this parameterized approximation often increases the number of parameters significantly, leading to the “curse of dimensionality” and inaccurate estimation. In this paper, we propose a novel and easily implemented approach to do variable selection in nonparametric models without parameterized approximation, enabling selection consistency to be achieved. The proposed method is applied to do variable selection for additive models. A two-stage procedure with selection and adaptive estimation is proposed, and the properties of this method are investigated. This two-stage algorithm is adaptive to the smoothness of the underlying components, and the estimation consistency can reach a parametric rate if the underlying model is really parametric. Simulation studies are conducted to examine the performance of the proposed method. Furthermore, a real data example is analyzed for illustration.

     

Functional ANOVA,ultramodularity and monotonicity: Applications in multiattribute utility theory

Utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision-maker’s preference structure. These properties are usually characterized via partial derivatives. However, elicitation methods do not necessarily lead to twice-differentiable utility functions. Furthermore, while in a single-attribute context concavity fully reflects risk aversion, in multiattribute problems such correspondence is not one-to-one. We show that Tsetlin and Winkler’s multivariate risk attitudes imply ultramodularity of the utility function. We demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion (functional ANOVA). The necessary and sufficient conditions under which monotonicity and/or ultramodularity of single-attribute functions imply the monotonicity and/or ultramodularity of the corresponding multiattribute function under additive, preferential and mutual utility independence are then established without reliance on the utility function differentiability. We also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision-maker’s multivariate risk attitudes.     

On efficient portfolio selection using convex risk measures

In this article we systematically revisit the classic portfolio selection theory in both of its branches, the determination of the efficient financial positions among such a choice set and the selection of the financial position which maximizes some utility function whose functional form involves some ‘measure of risk’. We study these problems by considering certain classes of convex risk measures and we show that for these classes the solution of the utility maximization problems in reflexive spaces take the form of a zero-sum game between the investor and the market.     

逐步增加首失效截尾样本下参数估计的优良性

在对称平方损失函数下, 利用逐步增加首失效截尾样本, 研究两参数Pareto分布族参数的一致最小方差无偏估计(UMVUE), Bayes估计和参数型经验Bayes(PEB)估计. 按照均方误差(MSE)准则, 比较UMVUE与PEB估计的优良性. 根据风险函数导出Bayes估计与PEB估计的渐近性, 并获得它们的收敛速度. 在相同的置信水平下, 研究参数分别在经典统计和Bayes统计中的区间估计, 并利用数值模拟说明Bayes区间估计的精度高于经典统计区间估计.     

Asymptotic efficient estimation in semiparametric nonlinear regression models

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On one method of finding the equilibrium state

An algorithm for solving a linear “production-exchange” model is described. The model reduces to a parametric model with strictly concave utility functions. Some properties of the parametric model are studied. Since the excessive demand map satisfies the discovered preference condition, it is possible to apply the second form of Chebyshev centers. For a sufficiently small parameter, the algorithm converges to the equilibrium state of the initial linear model. Bibliography:11 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 80, 1996, pp. 59–67.     

Multi-attribute non-expected utility

In management applications of risk theory, planning and decision making are typically concerned with complex multi-dimensional attributes of risk and utility trade-offs between them. This paper presents a novel approach to multi-attribute non-expected utility which is especially designed to serve application and risk management purposes. It is based on a recently developed non-expected utility model that accommodates systematic violations of expected utility of various kinds observed in risky choice experiments. In the model, the possible outcomes of risky decisions are assumed to be multi-dimensional, that is, classified, measured, compared and assessed from different economic and non-economic perspectives simultaneously. Of the risk attributes to be jointly evaluated in a decision problem, each is supposed to be utility independent of the complementary set of all the other attributes also considered. Mutual utility independence and additive independence are particularly pronounced forms of utility independence. An order-preserving preference functional exists if the agent??s risk preferences satisfy familiar rationality requirements. The functional provides a consistently scaled, multi-linear representation in terms of single-attribute probability-dependent utility functions. Finally, the formalism is applied to explain observed trade-offs between monetary benefits obtained, and fatalities incurred, in the operation of large-scale industrial systems.     

Sensitivity analysis incorporating fuzzy evaluation for scaling constants of multiattribute utility functions

A multiattribute utility function can be represented by a function of single-attribute utility functions if the decision maker’s preference satisfies additive independence or mutually utility independence. Additive independence is a preference condition stronger than mutually utility independence, and the multiattribute utility function is in the additive form if the former condition is satisfied, otherwise it is in the multiplicative form. In this paper, we propose a method for sensitivity analysis of multiattribute utility functions in multiplicative form, taking into account the imprecision of the decision maker’s judgment in the procedures for determining scaling constants (attribute weights).     

均值-CVaR零售商的供应链服务决策及协调契约

研究零售商具有风险偏好行为下,同时考虑价格、质量和服务水平的供应链联合决策问题。运用均值-CVaR准则来刻画零售商风险偏好行为,它包括风险厌恶、风险中性和风险追求,同时具有损失规避的特性。首先得到供应链集中系统、制造商提供服务（模型$\mbox{I}$）和零售商提供服务（模型$\mbox{II}$）下的最优决策和最优利润（期望效用）。其次,证明了成本共担契约在零售商风险厌恶时可以实现供应链协调.第三,对模型$\mbox{I}$和模型$\mbox{II}$协调后的最优利润（期望效用）进行比较,证明两种模型下制造商利润相同,而与模型$\mbox{I}$相比,模型$\mbox{II}$下零售商获得更多的期望效用。最后,数值例子证明了得到的研究结果。     

Minimax revisited. II

The global lower bound for the minimax risk proposed in Part I [12] is applied to the pointwise estimation of functions in the white Gaussian noise, under the squared losses. Some general ellipsoidal and cuboidal functional classes are discussed, including classes of entire functions of exponential type, Paley-Wiener classes of analytic functions, Sobolev classes and their modifications. Based on the proposed risk bounds, a numerical comparison of the minimax risks and the linear minimax risks is made. A nonasymptotic comparison of different types of functional classes is facilitated by their respective embeddings provided the classes are properly calibrated. This discussion demonstrates that the commonly perceived notion of a close connection between the smoothness of an unknown function and the accuracy of estimation can be misleading in a nonasymptotic setting. In particular, the notion of optimal rates of convergence, which has dominated nonparametric statistics for the last three decades, may no longer be productive.