Sharing the value‐at‐risk under distributional ambiguity

This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs, and shares the value‐at‐risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the worst‐case value‐at‐risk within a commonly agreed ambiguity set of the possible joint distributions. Through the lens of cooperative game theory, we show that this coalitional worst‐case value‐at‐risk is subadditive for the popular ambiguity sets in the distributionally robust optimization literature that are based on (i) convex moments or (ii) Wasserstein distance to some reference distributions. In addition, we propose easy‐to‐compute core allocation schemes to share the worst‐case value‐at‐risk. Our results can be readily extended to sharing the worst‐case conditional value‐at‐risk under distributional ambiguity.     

ASYMPTOTIC EQUIVALENCE OF RISK MEASURES UNDER DEPENDENCE UNCERTAINTY

In this paper, we study the aggregate risk of inhomogeneous risks with dependence uncertainty, evaluated by a generic risk measure. We say that a pair of risk measures is asymptotically equivalent if the ratio of the worst‐case values of the two risk measures is almost one for the sum of a large number of risks with unknown dependence structure. The study of asymptotic equivalence is particularly important for a pair of a noncoherent risk measure and a coherent risk measure, as the worst‐case value of a noncoherent risk measure under dependence uncertainty is typically difficult to obtain. The main contribution of this paper is to establish general asymptotic equivalence results for the classes of distortion risk measures and convex risk measures under different mild conditions. The results implicitly suggest that it is only reasonable to implement a coherent risk measure for the aggregation of a large number of risks with uncertainty in the dependence structure, a relevant situation for risk management practice.     

Robust risk aggregation with neural networks

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance.     

ONE-PARAMETER FAMILIES OF DISTORTION RISK MEASURES

This paper introduces parametric families of distortion risk measures, investigates their properties, and discusses their use in risk management. Their derivation is based on Kusuoka's representation theorem of law invariant and comonotonically additive coherent risk measures. Our approach is to narrow down a tractable class of risk measures by requiring their comparability with the traditional expected shortfall. We make numerical comparison among them and propose a method of estimating the value of the distortion risk measures based on data. Their use and interpretation in risk management will also be discussed.     

中小投资者的风险态度与市场环境

按照期望效用理论所揭示的风险厌恶、风险中性和风险追逐的3种风险态度的划分以及前景理论中投资者损失规避风险态度的特征,我们对我国A股市场投资者的风险偏好进行研究,发现在我国A股市场中小投资者风险态度受获得收益的显著影响,当投资者获得正收益时,总体呈现风险追逐,收益越高风险追逐的倾向越明显;当投资者获得负收益时,总体呈现风险中性,收益率与后市判断没有明显关系。我国中小投资者的风险态度不符合损失规避的特征。牛市环境下中小投资者总体呈现风险追逐,熊市环境下中小投资者总体风险中性。     

The Tax Incidence of Lotteries: Evidence from Five States

The nature of revenue generation for state‐sponsored lotteries has been an issue of public debate for quite some time. Although most studies have found lotteries to have a regressive tax incidence, several have concluded otherwise. Unfortunately, the vast majority of academic studies address this concern by examining the tax incidence of only one state's lottery and/or by using only one time period's data. In addition, many assessments of the tax impact of lotteries fail to consider other demographic variables that may influence purchase patterns and, thus, be of interest to policymakers. To remedy this, the current paper assesses the incidence of the lottery excise tax for five states using county level data spanning multiple years. Also assessed are changes in incidence across demographic groups as the lotteries matured. Lottery tax incidence is assessed with multiple regression estimates of the income elasticity of demand for lottery products. The predominant finding is that the lottery tax for these states had a regressive incidence. Otherwise, few consistencies in either change in lottery tax incidence or purchase patterns across demographic variables were found.     

Strategic intent and performance: The role of resource allocation decisions

The notion that a firm's strategic intent can affect its performance through managerial actions has become prominent in the organization literature. In this research, we propose that strategic aggressive firms will foster decisions that favor holding low levels of slack and low levels of R&D investments, resulting in increased firm ROI, and that a firm's risk preference will moderate the indirect effect of strategic intent on performance. Findings from moderated mediation analyses on data from 130 firms in manufacturing industries support our hypotheses. Specifically, the indirect effect of a firm's strategic intent on a firm's performance is moderated by its risk aversion, such that when risk aversion is high, the indirect effect of strategic intent on performance through slack is strengthened. Similarly, the indirect effect of strategic intent on firm performance through R&D investments is strengthened, when risk aversion is high.     

科技进步对央地政府间环评审批事权划分的影响--基于1997-2013年省级面板数据

我国政府间公共事务事权划分不仅参照效率原则,而且考虑政治风险因素。基于此逻辑,通过对环境治理事权细分并构建博弈模型,发现不同环境治理事权划分存在差异。具体到环评审批事权,其分权程度受地方科技水平的直接影响,本文采用省级面板数据对此进行实证检验,结果表明科技进步会促使中央下放环评审批事权,这也符合我国环评审批制度的改革历程。此外,中央政府不仅可以通过环境体制改革以降低政治风险,而且可以通过改变中央、地方和居民三者间环境偏好传导机制来改善环境治理效果。     

PORTFOLIO CHOICE VIA QUANTILES

A portfolio choice model in continuous time is formulated for both complete and incomplete markets, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers a wide body of existing and new models with law‐invariant preference measures, including expected utility maximization, mean–variance, goal reaching, Yaari's dual model, Lopes' SP/A model, behavioral model under prospect theory, as well as those explicitly involving VaR and CVaR in objectives and/or constraints. A solution scheme to this quantile model is proposed, and then demonstrated by solving analytically the goal‐reaching model and Yaari's dual model. A general property derived for the quantile model is that the optimal terminal payment is anticomonotonic with the pricing kernel (or with the minimal pricing kernel in the case of an incomplete market if the investment opportunity set is deterministic). As a consequence, the mutual fund theorem still holds in a market where rational and irrational agents co‐exist.     

INCORPORATING RISK AND AMBIGUITY AVERSION INTO A HYBRID MODEL OF DEFAULT

It is well known that purely structural models of default cannot explain short‐term credit spreads, while purely intensity‐based models lead to completely unpredictable default events. Here we introduce a hybrid model of default, in which a firm enters a “distressed” state once its nontradable credit worthiness index hits a critical level. The distressed firm then defaults upon the next arrival of a Poisson process. To value defaultable bonds and credit default swaps (CDSs), we introduce the concept of robust indifference pricing. This paradigm incorporates both risk aversion and model uncertainty. In robust indifference pricing, the optimization problem is modified to include optimizing over a set of candidate measures, in addition to optimizing over trading strategies, subject to a measure dependent penalty. Using our model and valuation framework, we derive analytical solutions for bond yields and CDS spreads, and find that while ambiguity aversion plays a similar role to risk aversion, it also has distinct effects. In particular, ambiguity aversion allows for significant short‐term spreads.     

MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set‐valued. Furthermore, it is reasonable to include the exchange rules in the argument of the risk measure and so consider risk measures of set‐valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set‐valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. We suggest a definition of the risk measure based on calling a set‐valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained selection risk measure is coherent (or convex), law invariant, and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In the case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set‐valued risk measures considered by Kulikov (2008, Theory Probab. Appl. 52, 614–635), Hamel and Heyde (2010, SIAM J. Financ. Math. 1, 66–95), and Hamel, Heyde, and Rudloff (2013, Math. Financ. Econ. 5, 1–28).     

Piracy on File-sharing Networks: Strategies for Recording Companies

In this article, we study the impact on piracy of selling music as downloadable files and the strategies that recording companies should adopt to increase profits. We find that total music sales and profits of firm (recording company) are higher, and total piracy (demand on file-sharing networks) is lower when the firm sells a downloadable version of a music track. We also look at the firm's optimal level of digital rights management (DRM) protection. We found that revenue decreases with increased protection. It is therefore optimal for the firm not to employ any DRM protection in the absence of network externality (NE). Listening to music or watching videos protected by DRM is cumbersome to users because they have to download license files and there are restrictions on the number of times the file can be copied and on the type of devices that can play the file. As a result, DRM protection is a disutility to the legal consumer and the firm must charge lower prices with more DRM protection. When NE is high and a nominal search cost is above a certain threshold, then non-zero protection becomes optimal.     

The Value of Information Integration in Meeting Delivery Dates

In this article, we consider the value of shared information within a business network. To make the problem concrete, we focus on a specific operational problem: How the final supplier to the customer determines promised delivery dates. In a traditional supply chain, the final supplier has little or no information on the delivery performance of intermediate suppliers and thus, has limited information with which to set delivery dates. On the other hand, in an information-integrated business network, the final supplier's enterprise resource planning (ERP) system can interact with all the intermediate suppliers' ERP systems to determine exactly how far ahead or behind schedule the network is in meeting the needs of a specific customer. This information should improve the final supplier's ability to set realistic delivery dates. We attempt to quantify the value of this information and determine precisely why it is valuable so that management can best exploit information integration.

We use a modeling approach in this research, beginning with simple analytic models and progressing to more realistic simulation models. Our analytic model establishes an important principle: Information integration not only significantly improves the average on-time delivery performance of a business network, but also dramatically improves its worst-case performance. Because customer dissatisfaction is generally associated with worst-case performance, information integration may be highly beneficial even if its effect on average on-time delivery is small. Simulation models allow us to compare the performance of more realistic business networks. These models suggest, for example, that the value of information integration is dependent on both the structure of the network itself (whether serial or arborescent) and on the typical customer order date in the production cycle. These insights allow us to begin to identify the types of business networks in which information integration will have the highest value.     

The influence of entrepreneurial marketing processes and entrepreneurial self-efficacy on community vulnerability,risk, and resilience

This paper uses the 2010/2011 Christchurch earthquake and re-development efforts as an exemplar to explore how entrepreneurial marketing processes combined with entrepreneurial self-efficacy can be leveraged to help a community reduce its vulnerability to natural disasters and enhance its resilience. Manyena's (Manyena, S. B. (2006). The concept of resilience revisited. Disasters, 30, 433–450; Manyena, S. B. (2012). Disaster and development paradigms: Too close for comfort? Development Policy Review, 30, 327–345) vulnerability–resilience theory is used as the conceptual framework to delineate the prophylactic benefits of building a community's entrepreneurial marketing process capabilities and the notion of entrepreneurial self-efficacy as defensive mechanisms to mitigate the effect of disasters. This work has resulted in an augmented disaster risk equation that considers: (1) the risk that a natural disaster poses on a community (as a function of the vulnerability of the community's tangible assets); (2) the hazard potential of the disaster; and (3) the resilience of its social and economic systems. This paper develops a measure of the symbiotic interrelationship of a community's entrepreneurial marketing process capabilities and community-level entrepreneurial self-efficacy to illustrate how leveraging the entrepreneurial, marketing, social, and engineering educational resources of a community can create a less vulnerable and more resilient community. In doing so, the paper develops a set of research propositions to guide future research and policy.     

A Portable DRM Scheme Using Smart Cards

The Internet is a relatively friendly and convenient environment for allowing music, audio, video files, and other digital contents to be copied, modified, and distributed easily. Nevertheless, from the point view of content owners, copyrights protection and intellectual property rights are critical issues that involve revenue loss. The current digital rights management (DRM) systems provide an acceptable copyright protection solution. The DRM venders usually provide a function allowing consumers to migrate their authorized license from one device to another. Still, this function is restricted by the device type and network domain, which does not completely satisfy consumers' needs. However, a successful DRM system should make consumers willing to use it. Therefore, improving copyright protection convenience for consumers is a significant issue. In this paper, a portable DRM scheme in which the usage-rights follow the consumer, but not the device, is presented for constructing a flexible DRM system that improves portability, therefore allowing users to have content use rights on any devices. In addition, an awkward storage system for encrypted data does not need to be maintained by the proposed scheme, thereby giving a more secure, cost-effective solution.     

科技风险与公众对科学的信任

在当前科学技术成为最大风险源的风险社会中,我们应当关注公众对科学的信任问题,其与科技风险问题密切相关。一方面,科技风险的出现使得公众对科学的信任面临挑战;另一方面,由于科技风险的存在,公众对科学的合理信任又有着重要的意义。因此,在科技风险的社会中,我们应该积极构建公众对科学的合理信任。     

Intrafirm causal ambiguity in an international context

This paper examined the incidence of intrafirm causal ambiguity in the management's perception concerning the critical drivers of their firms’ performance. Building on insights from the resource-based view we developed and tested hypotheses that examine (1) linkage ambiguity as a discrepancy between perceived and measured resource–performance linkages, (2) characteristic ambiguity for resources and capabilities with a high degree of complexity and tacitness, and (3) the negative association between linkage ambiguity and performance. The observations based on the explicit perceptions of 356 surveyed managers were contrasted with the empirical findings of the resource/performance relationship derived by structural equation modelling from the same data sample. The findings validate the presence of linkage ambiguity particularly in the case of resources and capabilities with higher degree of characteristic ambiguity. The findings also provide empirical evidence in support of the advocacy for a negative relationship between intrafirm causal ambiguity and performance. The paper discusses the potential reasons for the disparities between empirical findings and management's perceptions of the key determinants of export success and makes recommendations for future research.     

A NOTE ON THE QUANTILE FORMULATION

Many investment models in discrete or continuous‐time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original investment problem. Under certain monotonicity assumptions, several schemes to solve such quantile optimization problems have been proposed in the literature. In this paper, we propose a change‐of‐variable and relaxation method to solve the quantile optimization problems without using the calculus of variations or making any monotonicity assumptions. The method is demonstrated through a portfolio choice problem under rank‐dependent utility theory (RDUT). We show that this problem is equivalent to a classical Merton's portfolio choice problem under expected utility theory with the same utility function but a different pricing kernel explicitly determined by the given pricing kernel and probability weighting function. With this result, the feasibility, well‐posedness, attainability, and uniqueness issues for the portfolio choice problem under RDUT are solved. It is also shown that solving functional optimization problems may reduce to solving probabilistic optimization problems. The method is applicable to general models with law‐invariant preference measures including portfolio choice models under cumulative prospect theory (CPT) or RDUT, Yaari's dual model, Lopes' SP/A model, and optimal stopping models under CPT or RDUT.     

RISK-AVERSION BEHAVIOR IN CONSUMPTION/INVESTMENT PROBLEMS1

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type function in the special case treated in the paper. Coefficients of absolute and relative risk aversion are defined to be the well-known curvature measures associated with the derived utility of wealth obtained as the value function of the agent's optimization problem. Through an analysis of these coefficients, we show how the change in agent's risk aversion as his wealth changes depends on his consumption utility and the other problem parameters, including the payment at bankruptcy. Moreover, in the HARA case, we can conclude that the agent's relative risk aversion is nondecreasing with wealth, while his absolute risk aversion is decreasing with wealth only if he is sufficiently wealthy. At lower wealth levels, however, the agent's absolute risk aversion may increase with wealth in some cases.     

资本配置扭曲与民营企业出口生存

面对出口贸易限制增多的压力，提升我国民营企业出口生存概率具有重要的现实意义。通过考察资本配置扭曲对我国民营企业出口生存时间和生存概率的影响效应、渠道和后果。结果发现：民营企业的出口市场进入率和退出率高于国有企业，民营企业在出口4年以后生存率大幅下降；资本配置扭曲程度越高则民营企业退出出口市场的概率越大、生存时间越短；从驱动因素来看，全要素生产率提升和资本密集度下降是资本配置扭曲降低民营企业出口生存率的重要渠道；异质性分析表明，资本配置扭曲提高对沿海城市、资本密集型以及2002年以后民营企业出口危险率的促进作用更大。