A note on utility‐based futures hedging performance measure

This note considers the estimator for the utility‐based hedging performance. It shows that the estimator incurs a downward bias, regardless of whether the conventional mean‐variance expected utility function or the more general risk‐averse utility function is adopted. Consequently, the usefulness of the futures contract is under‐estimated. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Asset preference,skewness, and the measurement of expected utility

This article shows that serious analytical errors may occur in expected utility theory when Taylor series approximation methods are used without careful attention to underlying mathematical assumptions. Recent studies have developed theory incorporating skewness of return into expected utility calculations based on a Taylor series approximation. It is apparent that this theory is invalid if assumptions for application of a Taylor series cannot be met. Errors may occur if returns fall outside the region of convergence of the utility function ot if the partial sums of the Taylor series provide poor approximations to the utility function. Stylized examples are presented to illustrate miscalculation of utility when the various assumptions are violated. These examples are motivated by the use of Taylor series approximations in current literature which deal with the new spectrum of financial securities.     

OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITY

We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank‐dependent expected utility (RDEU) theory with a concave utility function and an inverse‐S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.     

UTILITY MAXIMIZATION IN A LARGE MARKET

We study the problem of expected utility maximization in a large market, i.e., a market with countably many traded assets. Assuming that agents have von Neumann–Morgenstern preferences with stochastic utility function and that consumption occurs according to a stochastic clock, we obtain the “usual” conclusions of the utility maximization theory. We also give a characterization of the value function in a large market in terms of a sequence of value functions in finite‐dimensional models.     

OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY-BASED PRICING

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies—those strategies whose wealth process is a super-martingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem. We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.     

效用理论在保险决策中的应用

效用函数的凹凸性将风险态度进行了三类划分：风险中性型、风险厌恶型、风险喜好型。本文从效用理论出发研究了不同的风险态度决策人的不同的风险决策结果,讨论了效用理论在保险产品的定价中的应用,并根据不同的风险态度和不同的损失分布函数确定最优投保方式.     

论民营银行成长的逻辑——一个基于国家效用函数的分析框架

中国金融制度变迁具有政府强制性与渐进式等特征,因此从国家金融方面的效用函数结构变动的视角来探究中国民营银行的成长逻辑,无疑是关键和有益的。运用规则经济学中的国家理论与制度变迁原理,在已有研究的基础上构建一个国家效用函数,并从此效用函数的动态变化,论证中国民营银行成长的内在动机与逻辑。     

Fully nonmetric estimation of a continuous nonlinear conjoint utility function

The special conjoint-analysis problem of estimating the parameters of a continuous nonlinear utility function from ordinal rank order data is investigated. A special purpose estimation method, called NONCON, is proposed that offers two advantages: First, it is capable of directly maximizing Kendall's rank order correlation coefficient T as the appropriate measure of goodness of fit. Second, it requires less computational effort than competing procedures using general purpose conjointanalysis programs. The superiority of NONCON is demonstrated for the estimation of a continuous nonlinear two-parameter utility function the parameters of which serve as input for the optimization of sales force compensation schemes.     

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.     

Why do European consumers smoke? Responses from the rational addiction model

In this paper, we test whether European consumers are addictive smokers and, if this is the case, then whether such addictions can be explained by the rational addiction theory. To this end, we start from a non‐separable intertemporal utility function, which allows us to derive a demand function that is estimated using tobacco time‐series. The results are in accordance with the model of rational addiction for all European smokers. Thus, we observe the addictive character of tobacco consumption and, secondly, we note that the addiction is not the result of myopic consumer behaviour, but rather of the maximization of total utility, implying that consumers consider the future effects of their current decisions.     

Modelling pedestrian go-home decisions: A comparison of linear and nonlinear compensatory,and conjunctive non-compensatory specifications

This paper presents the main findings of an application of several models to predict the go-home decision of pedestrians in shopping streets. Two compensatory multinomial logit models, one with a linear utility function of time and the other with a nonlinear utility function of time, and a non-compensatory conjunctive model are specified. Data about pedestrian behaviour in a major shopping street in Beijing served as input for model estimation. The conjunctive model performs best, suggesting that pedestrians use simplifying heuristics to decide when to end the shopping trip and go home. In addition, the nonlinear multinomial logit model outperforms the linear model, indicating that marginal utility of time decreases with increasing time.     

Convergence of optimal expected utility for a sequence of discrete‐time markets

We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The nth discrete‐time economy is generated by a scaled n‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support. We confirm Kreps' conjecture if the consumer's utility function U has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function U with asymptotic elasticity equal to 1, for ζ such that .     

Representing Heterogeneity in Consumer Response Models 1996 Choice Conference Participants

We define sources of heterogeneity in consumer utility functions relatedto individual differences in response tendencies, drivers of utility, formof the consumer utility function, perceptions of attributes, statedependencies, and stochasticity. A variety of alternative modelingapproaches are reviewed that accommodate subsets of these various sourcesincluding clusterwise regression, latent structure models, compounddistributions, random coefficients models, etc. We conclude by defining anumber of promising research areas in this field.     

MEAN–VARIANCE PORTFOLIO CHOICE: QUADRATIC PARTIAL HEDGING

In this paper we investigate the problem of mean–variance portfolio choice with bankruptcy prohibition. For incomplete markets with continuous assets' price processes and for complete markets, it is shown that the mean–variance efficient portfolios can be expressed as the optimal strategies of partial hedging for quadratic loss function. Thus, mean–variance portfolio choice, in these cases, can be viewed as expected utility maximization with non-negative marginal utility.     

A Generalized Cameron–Martin Formula with Applications to Partially Observed Dynamic Portfolio Optimization

The optimal dynamic allocation problem for a Bayesian investor is addressed when the stock's drift—modeled as a linear mean-reverting diffusion—is not observed directly but only via the measurement process. Adopting a martingale approach, an appropriate generalization of the Cameron–Martin (1945) formula then enables computation of both the optimal dynamic allocation and the value function for a general utility function, in terms of an inverse Laplace transform of an explicit expression. Moreover, closed-form formulas are provided in the case of power utility.     

The impact of membership fees on consumer attitude and choice

This study examined the impact of membership fees on consumer attitude and purchase behavior. Subjects participated in a computerized simulated shopping experiment, and chose between three competing videotape rental stores, receiving feedback about purchase utility on each occasion. Manipulations included the presence or absence of an initial membership-fee requirement at the dominant store and the timing of a lowering of that store's utility to the same level as that offered by a competing establishment. Store loyalty is shown to vary as a function of membership fees and utility changes in a manner consistent with hypotheses generated from prospect, escalation-of-commitment, cognitive-dissonance, and self-perception theories. © 1998 John Wiley & Sons, Inc.     

PROBABILITY AND UNCERTAINTY: THE LEGACY OF GEORGESCU‐ROEGEN

In this paper we consider Georgescu‐Roegen's approach to uncertainty, showing that his characterization of expectations cannot be reduced to any probabilistic decision‐making model. Drawing upon Georgescu‐Roegen's lesson a lexicographical utility function is proposed and analysed in the mark of his own peculiar scientific methodology. It is demonstrated that such a formulation can be useful in solving the usual failure of the expected utility model, such as the Ellsberg paradoxes. The epistemic limits of our re‐construction are considered.     

A Discrete‐Time Intertemporal Asset Pricing Model: GE Approach with Recursive Utility

This paper studies the equilibrium characterization of asset pricing in a discrete‐time Lucas exchange economy (Lucas 1978) with the intertemporal recursive utility function of Epstein and Zin (1989). A general formulation of equilibrium asset pricing is presented. It is shown that risk aversion of a certainty equivalent corresponds to risk aversion in the intertemporal asset pricing model. The discrete‐time analogue of Ma's (1993) option pricing formula is derived in an i.i.d. environment, with which we prove an observational nonequivalence theorem in distinguishing the differences of the betweenness recursive utility functions and the expected utility functions. Additionally, when the consumption growth rate follows a first-order Markov process, it is shown that the observational nonequivalence result holds for Kreps–Porteus expected utility. Finally, as by-products, this paper also contains derivations of closed-form formulas for the aggregate equity (with endogenously determined yields), the term structure of interest rates, and European call options on the aggregate equity in a Markov setting.     

Generalized Ordered Weighted Reference Dependent Utility Aggregation Operators and Their Applications to Group Decision-Making

To quantify the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. RUs include S-shaped RU and non-S-shaped RU. Each RU affords a framework where the psychological factors explicitly enter the decision problem via the basic utility function, reference point and loss aversion coefficient. Under the general framework, we derive a generalized ordered weighted S-shaped RU proportional averaging (GOSP) operator and a generalized ordered weighted non-S-shaped RU proportional averaging (GONSP) operator, respectively. The GOSP operator implies the risk attitude of the DM for relative losses is risk-seeking, while GONSP operator indicates the risk attitude in this case is risk-averse. As a special case, GONSP operator can degenerate into GOWPA operator which means that the attitude of the DM is risk-neutral. Each operator satisfies the desirable properties of general operator, i.e., monotonicity, commutativity, idempotency and boundedness. Furthermore, we consider hyperbolic absolute risk aversion (HARA) function as the basic utility function, and define an S-shaped HARA and a non-S-shaped HARA utility functions. Based on the two new RUs, we propose GOSP–HARA operator and GONSP–HARA operator. Every operator covers many existing aggregation operators. To ascertain weights of such operators, the paper builds an attribute-deviation weight model and a DMs-deviation weight model. Based on these RU operators and weight models, an approach is addressed for solving multiple attribute group decision-making problem. At last, an example is provided to show the feasible of our approach.