结构性金融产品的定价与投资决策研究：不确定性方法

本文在不确定性框架下,利用Choquet定价和Choquet期望效用理论研究结构性金融产品的定价和投资问题．并将不确定性参数和复杂系数对产品定价和投资决策的影响进行了敏感性分析,主要结论有随着不确定性程度的提高,产品的定价水平也随之提高;复杂产品有利于分散产品的集中风险且投资者对复杂产品平均预期收益水平的估计较高,从而选择复杂产品而非简单产品,部分解释了传统文献中结构性金融产品定价过高和投资者偏好复杂产品而非简单产品的两个悖论。     

时间对人们效用影响的理论进展

预期效用理论一直是微观经济领域的重要支柱之一，也是现代金融理论的重要理论基础，它给出了不确定性条件下理性行为的描述。期望理论是新近兴起的一种非预期效用理论，对很多预期效用理论无法解释的现象提供了合理解释。     

经济学中的不确定性和有限理性

经典期望效用理论不能为现实中的不确定性决策和有限理性行为提供具有描述意义的指导,解决这一问题需要在期望效用理论之外寻找新的思路。不确定性的本质在于决策者自身不知道相关概率分布,他的决策依据是自己确定的主观概率。尝试模型化不确定性的非期望效用理论需要正视这类决策中的"主观性"。而现实中不确定性环境下的具体决策过程呈现出有限理性甚至"非理性"特征,由此导致的宏微观经济效应也难以在期望效用理论框架下进行考察。关注"真实世界"的经济学应该对此给予更多的注意力。     

期望效用理论与前景理论的一致性

经济中存在着大量的不确定性,人们在不确定情况下的决策行为是公司资本结构、期权定价等问题的理论基础.自从冯?诺伊曼和摩根斯坦的经典著作《博弈论和经济行为》问世以来,期望效用理论一直被奉为理性人在不确定情况下进行决策的准则,在期望效用理论的基础上,建立起了资本资产定价模型、有效市场等一系列经济理论.然而随着实验经济学的发展,经济学家发现人们在实际决策中会出现一些违反期望效用准则的异象.1979年,卡尼曼和特沃斯基的论文前景理论,解释了这些异象,并成为行为金融学的理论基础.该文在介绍这两种理论主要思想的基础上证明,在一个理性人应当遵循的代数结合律公理的条件下,前景理论和期望效用理论的结论是一样的.     

广义随机占优理论——一种群体决策理论

本文以广义期望效用———RDEU模型为基础 ,推广了传统随机占优和“对偶随机占优”理论 ,提出了一种新的不确定性条件下的群体决策理论———广义随机占优理论。通过引入高阶转换函数和高阶(条件 )期望效用概念 ,本文给出了风险厌恶者、风险爱好者、悲观主义者、乐观主义者广义随机占优定义及其充要条件 ,我们将这种研究思路称为经典方法。最后讨论了广义随机占优理论在经济研究和管理实践中的应用前景。     

基于信息修正的非期望效用模型

人们对事件发生的可能性存在着主观判断。在不同的概率区间,人们对概率变化的敏感度是不一样的。传统的期望效用理论忽视了决策者对概率的主观反应,无法准确描述风险决策行为。基于信息修正的非期望效用模型,将客观概率转换成主观决策权重,可以弥补期望效用模型在捕捉决策者对概率主观反应方面的缺陷;同时,利用基于信息修正的非期望效用模型,通过量化人们在购买保险或股票时对风险的主观概率判断,可以对人们的保险需求和证券投资行为作出更好的解释或预测。     

效用理论下的零效用保费浅析

本文分析的是期望效用理论和等级依赖效用理论下的零效用保费。文章从简述期望效用理论出发 ,从效用原理角度阐述了保险定价的基本原则 ,以及零效用下保费的计算 ,介绍了等级依赖效用理论下的保险定价的零效用保费及其基本特征     

马科维兹资产组合选择理论评述

马科维兹,发展了投（个人或机构）在不确定性条件下配置金融资产的理论,即证券投资组合理论。这一理论分析了财富如何能最优地投资于期望收益率和风险不同的效益,即投资为追求效用最大化而寻找最优投资组合。     

知识交易的定价

就知识经济理论而言,知识交易是不应该被忽略的关键性主题。根据知识供给者面对的市场不同,知识交易的定价分析方法也不同。定价模型揭示了效用不确定性、效用的动态性、信息不对称、非重复交易、交易方式的多样性等对最优定价以及社会福利的影响。知识交易理论是知识经济学的微观基础。     

论奥曼在重复博弈领域中的开创性研究

奥曼教授开创性的定义了“博弈论”的概念，并最早把在可转移效用中广泛应用的“稳定集”和“核心”的定义扩充到了非转移效用领域，同时指出博弈论中的非转移效用值不一定是唯一确定的。在此基础上，促进了在更一般的不完全信息的重复博弈理论领域中的研究。     

The Choquet Bargaining Solutions

We axiomatically investigate the problem of rationalizing bargaining solutions by social welfare functions that are linear in every rank-ordered subset of Rⁿ₊ . Such functions, the so-called Choquet integrals, have been widely used in the theories of collective and individual choice. We refer to bargaining solutions that can be rationalized by Choquet integrals as Choquet bargaining solutions. Our main result is a complete characterization of Choquet bargaining solutions. As a corollary of our main result, we also obtain a characterization of the generalized Gini bargaining solutions introduced by Blackorby et al. (1994, Econometrica62, 1161–1178). Journal of Economic Literature Classification Numbers: D71, C78.     

Eliciting the core of a supermodular capacity

Summary. The paper utilizes duality theory to derive an exact representation of the core of a supermodular capacity for finite-state-space Choquet expected utility preferences. Using the dual representation we develop an algorithm that uses information on willingness to pay and willingness to sell to elicit a supermodular capacity in a finite number of iterations.Received: 21 February 2003, Revised: 26 May 2004, JEL Classification Numbers: D81. Correspondence to: Robert G. ChambersThe authors thank J. Quiggin and an anonymous referee for comments that improved the paper.     

Precautionary principle as a rule of choice with optimism on windfall gains and pessimism on catastrophic losses

The paper investigates a decision-making process involving both risk and ambiguity. Differently from existing papers [Basili, M., Chateauneuf, A., Fontini, F., 2005. Choices under ambiguity with familiar and unfamiliar outcomes, Theory and Decision 58, 195-207; Chichilnisky, G., 2000. Axiomatic approach to choice under uncertainty with catastrophic risks. Resources and Energy Economics 22, 221-231; Chichilnisky, G., 2002. In: El-Shaarawi, A.,H., Piegorsch, W.W. (Eds.), Catastropic Risks. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd, Chichester, UK, pp. 274-279], we assume that, in a Choquet Expected Utility framework, the decision-maker is pessimistic with respect to unfamiliar (catastrophic) losses, optimistic with respect to unfamiliar (windfall) gains and ambiguity-neutral with respect to the familiar world. A representation of the decision-maker's choice is obtained that mimics the Restricted Bayes-Hurwicz Criterion. In this way a characterization of the Precautionary Principle is introduced for decision-making processes under ambiguity with catastrophic losses and/or windfall gains.     

Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet–Brownian motions

Ambiguity is pervasive in many environments and is increasingly being introduced into economic and financial models. This paper characterises ambiguity in the form of newly defined Choquet random walks: discrete-time binomial trees with capacities instead of exact probabilities on their branches. We describe the axiomatic basis of Choquet random walks, including dynamic consistency. We also discuss the convergence of Choquet random walks to Choquet–Brownian motion in continuous time. In contrast to previous literature, we derive tractable stochastic processes that allow for a wide range of ambiguity preferences to be represented in continuous time (including ambiguity-seeking preferences). Finally, we apply Choquet–Brownian ambiguity to a model of stationary inter-temporal portfolio choice. We find that both the mean and the variance of the underlying stochastic process are modified. This result opens the way for qualitative and quantitative results that differ from those of standard expected utility models and other models that feature ambiguity.     

Half empty, half full and why we can agree to disagree forever

Aumann [Aumann R., 1976. Agreeing to disagree. Annals of Statisitics 4, 1236–1239] derives his famous we cannot agree to disagree result under the assumption that people are expected utility (=EU) decision makers. Motivated by empirical evidence against EU theory, we study the possibility of agreeing to disagree within the framework of Choquet expected utility (=CEU) theory which generalizes EU theory by allowing for ambiguous beliefs. As our first main contribution, we show that people may well agree to disagree if their Bayesian updating of ambiguous beliefs is psychologically biased in our sense. Remarkably, this finding holds regardless of whether people with identical priors apply the same psychologically biased Bayesian update rule or not. As our second main contribution, we develop a formal model of Bayesian learning under ambiguity. As a key feature of our approach the posterior subjective beliefs do, in general, not converge to “true” probabilities which is in line with psychological evidence against converging learning behavior. This finding thus formally establishes that CEU decision makers may even agree to disagree in the long-run despite the fact that they always received the same information.     

A new integral for capacities

A new integral for capacities is introduced and characterized. It differs from the Choquet integral on non-convex capacities. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between the minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also in cases where the information available is limited to a few events. I wish to thank Eran Hanany, David Schmeidler, Eilon Solan and especially Yaron Azrieli and the anonymous referee of Economic Theory for their helpful comments.     

Informational efficiency with ambiguous information

This paper proves the existence of fully revealing rational expectations equilibria for almost all sets of beliefs when investors are ambiguity averse and have preferences that are characterized by Choquet expected utility with a convex capacity. The result implies that strong-form efficient equilibrium prices exist even when many investors in the market make use of information in a way that is substantially different from traditional models of financial markets.     

Foundations of neo-Bayesian statistics

We study an axiomatic model of preferences, which contains as special cases Subjective Expected Utility, Choquet Expected Utility, Maxmin and Maxmax Expected Utility and many other models. First, we give a complete characterization of the class of functionals representing these preferences. Then, we show that any such functional can be represented as a Choquet integral

where is the canonical mapping from the space of bounded Σ-measurable functions into the space of weak^*-continuous affine functions on a weak*-compact, convex set of probability measures on Σ. Conversely, any preference relation defined by means of such functionals satisfies the axioms of the model we study. Different properties of the capacity give rise to different models. Our result shows that the idea of Choquet integration is general enough to embrace all the models mentioned above. In doing so, it widens the range of applicability of well-known procedures in robust statistics theory such as the Neyman–Pearson lemma for capacities [P.J. Huber, V. Strassen, Minimax tests and the Neyman–Pearson lemma for capacities, Ann. Statist. 1 (1973) 251–263], Bayes' theorem for capacities [J.B. Kadane, L. Wasserman, Bayes' theorem for Choquet capacities, Ann. Statist. 18 (1990) 1328–1339] or of results like the Law of Large numbers for capacities [F. Maccheroni, M. Marinacci, A strong law of large numbers for capacities, Ann. Probab. 33 (2005) 1171–1178].     

Axiomatic characterizations of the Choquet integral

Summary. The Choquet integral is an integral part of recent advances in decision theory involving non-additive measures. In this article we present two new axiomatic characterizations of this functional. Received: January 27, 1997; revised version: April 28, 1997     

Diversification, convex preferences and non-empty core in the Choquet expected utility model

Summary. We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely “sure diversification.” We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index. Received: July 27, 1999; revised version: November 7, 2000