Expected Utility Criterion Research Articles

Partial identification and mergers

This paper discusses policy choice under ambiguity in the context of merger simulation. We do so by incorporating the uncertainty about post-merger conduct into a simple merger simulation model. We isolate the problem of uncertainty regarding post-merger conduct by working with a simple “conduct parameters” model in the spirit of Bresnahan (1982) and Lau (1982). We then apply Manski’s (2011) analysis, and discuss policy choice under the maxmin, minimax-regret, and expected utility criteria.

Portfolio Performance Maximization with Generalized Kappa Ratio

We examine the maximization problem of performance measure of financial structured products. For this purpose, we introduce the Kappa ratios, based on downside risk measures which take account of the asymmetry of the return probability distribution. First, we deal with the optimization of some standard structured portfolios. We examine in particular the optimal combination of risk free, stock and call/put instruments with respect to Kappa performance measures and in particular to the SharpeOmega ratio. Then, we provide the general solution of the optimal positioning problem with respect to Kappa ratios. We analyze its properties and compare it to the portfolio profile that is optimal with respect to the standard expected utility criterion.

Uniform expected utility criteria for decision making under ignorance or objective ambiguity

We provide an axiomatic characterization of a family of criteria for ranking completely uncertain and/or ambiguous decisions. A completely uncertain decision is described by the finite set of all its consequences. An ambiguous decision is described as a finite set of possible probability distributions over a finite set of prizes. Every criterion in the characterized family can be thought of as assigning to every consequence (probability distribution) of a decision an equal probability of occurrence and as comparing decisions on the basis of the expected utility of their consequences (probability distributions) for some utility function.

Single-period inventory model with discrete stochastic demand based on prospect theory

This paper studies a single-period inventory (newsvendor) problem with discrete stochastic demand. In general, most of the previous works are based on the expected profit/cost criterion or expected utility criterion. We consider the effect of irrational factor under uncertainty and therefore incorporate prospect theory into inventory model. Our objective is to maximize the overall value of the prospect, which can be calculated by using the value function and the weighting function. For any given initial inventory level, it can be shown that a state-dependent order-up-to policy is optimal. Further, the optimal policy has a simple structure, and the retailer can easily decide whether to place an order or not. Moreover, the impacts of parameters on the optimal policy are illustrated through numerical experiments.

Robust Incentives for Information Acquisition

A principal needs to make a decision. An expert is able to supply information that is helpful to the principal, but only by exerting effort, which is costly. The principal can incentivize the expert to put in effort by paying him a reward based on his reported information and on the true state of nature, which is revealed ex post. There is limited liability - payments can never be negative. The principal is uncertain about the expert's information acquisition technology: she knows some actions (experiments) that he can take to obtain information, but there may also be other experiments available. In the face of this uncertainty, the principal evaluates any incentive contract she may offer using a maxmin expected utility criterion. Under quite general conditions, we show that the optimal contract is a restricted investment contract, in which the expert chooses from a subset of the decisions available to the principal, and is then rewarded proportionally to the value of his designated decision in the realized state (although the decision that the principal actually makes need not be the same as the one designated by the expert).

Economic Analysis of Summer Fallow Management to Reduce Take-All Disease and N Leaching in a Wheat Crop Rotation

This paper addresses the question of summer cover-crop adoption by farmers in presence of a risk of yield loss due to take-all disease and climate variability. To analyze the public incentives needed to encourage farmers to adopt summer cover crops as a means of reducing N leaching, we combine outputs from an economic, an epidemiological and an agronomic model. The economic model is a simple model of choice under risk. The farmer is assumed to choose among a range of summer fallow managements and input uses on the basis of the expected utility criterion (HARA assumption) in presence of both climate and take-all risks. The epidemiological model proposed by Ennaïfar et al. (Eur J Plant Pathol 118:127–143, 2007) is used to determine the impact of take all on yields and N uptake. The crop-soil model (STICS) is used to compute yield developments and N leaching under various management options and climatic conditions. The input parameters are chosen to match the conditions prevailing in Grignon, located in the main wheat-growing area in France. Eight management systems are examined: four summer fallow managements: ‘wheat volunteers’ (WV), ‘bare soil’ (BS), ‘early mustard’, ‘late mustard’, and two input intensities. We show that the optimal systems are BS (WV) when the take-all risk is (not) taken into account by agents. We then compute the minimum payment to each system such that it emerges in the optimum. We thus derive the required amounts of transfer needed to trigger catch-crop adoption. The results of the Monte Carlo sensitivity analysis show that the ranking of management systems is robust over a wide range of input parameters.

Bayesian selection of multiresponse nonlinear regression model

A Bayesian method for the selection and ranking of multiresponse nonlinear regression models in a given model set is proposed. It uses an expected utility criterion based on the logarithmic score of a posterior predictive density of each model. Two approaches are proposed to get this posterior. The first is based on a general asymptotically convergent approximation of the model parameter posterior corresponding to a wide class of parameter priors. The second, a numerical one, uses well-known pure or hybrid MCMC methods. Both posterior approximation approaches allow the practical computation of the expected utility criterion on a sample-reuse basis. This leads to a class of Bayesian cross-validation (CV) procedures, aiming at finding the model having the best predictive ability among a set of models. Varied comparisons of the performances of the Bayesian procedures, with that of AIC, BIC and standard CV procedures, are proposed on a simulated and a real model selection problem case studies, of low and high parametric dimensions respectively.

Ranking discrete outcome alternatives with partially quantified uncertainty

Real decision makers (DM) partially quantify uncertainty as probability uncertainty intervals. Then alternatives are modeled as fuzzy-rational lotteries. Those can be approximated by standard lotteries with point-estimate probabilities, referred as classical-risky. Ranking the approximating classical-risky lotteries is a problem under risk, solved by expected utility. However, the approximation itself is a problem under strict uncertainty. Here this part of the problem is solved by criteria under strict uncertainty, which if not perfectly rational, are well worked descriptive methods with known properties. The proposed Laplace, Wald, maximax and Hurwiczα expected utility criteria for prescriptive ranking of fuzzy-rational lotteries allow the DM to control the approximation of alternatives with partially quantified uncertainty in consistency with her/his degree of belief and with his optimism–pessimism attitude. That makes them superior to the widespread abandoned-m and normalized mean criteria, which often violate the intrinsic subjective probabilities of the DM. The proposed criteria are generalizations of expected utility criterion under risk and of their standard versions under strict uncertainty.

Remarks on “A measure of risk and a decision-making model based on expected utility and entropy” by Jiping Yang and Wanhua Qiu (EJOR 164 (2005), 792–799)

Yang and Qiu [Yang, J., Qiu, W., 2005. A measure of risk and a decision-making model based on expected utility and entropy. European Journal of Operational Research 164, 792–799] suggest a new concept for decision making under risk. This concept relies on a combination of the well-known expected utility criterion and the so-called entropy. The authors claim that the approach might be used as a descriptive as well as a normative decision model. In this paper, the theoretical soundness of the concept of entropy is critically examined. The analysis is underpinned by a discussion of the properties of the respective entropy function. Furthermore, normative and descriptive features of the concept are discussed and it is shown that the usefulness with respect to both aspects is questionable.

Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria

This paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer. Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.

Real option analysis of a technology portfolio

This article contributes to methodology of real options analysis of investments in capital intensive process industries, where relatively homogenous outputs are produced using commonly known production technologies. In addition to capacity expansion, the method can be used for analysis of mergers and acquisitions. Valuation of the real option is based on bid price; i.e., the maximum price the firm is willing to pay. To find such a price, stochastic optimization with an expected utility criterion is used to determine investments in product specific technologies as well as in publicly traded financial instruments (the competing investments). To operationalize the valuation principle, we develop a double binary tree employing Kalman filter for scenario generation. For exponential utility, valuation is carried out by dynamic programming. We extend known methods to allow interdependence of the mill cash flow and return on competing financial investments. For forest industries, we provide an illustration, where the underlying price process in our Kalman filter application is a vector error correction model.

Bayesian Multioutput Feedforward Neural Networks Comparison: A Conjugate Prior Approach

A Bayesian method for the comparison and selection of multioutput feedforward neural network topology, based on the predictive capability, is proposed. As a measure of the prediction fitness potential, an expected utility criterion is considered which is consistently estimated by a sample-reuse computation. As opposed to classic point-prediction-based cross-validation methods, this expected utility is defined from the logarithmic score of the neural model predictive probability density. It is shown how the advocated choice of a conjugate probability distribution as prior for the parameters of a competing network, allows a consistent approximation of the network posterior predictive density. A comparison of the performances of the proposed method with the performances of usual selection procedures based on classic cross-validation and information-theoretic criteria, is performed first on a simulated case study, and then on a well known food analysis dataset.

Robust projections in the class of martingale measures

Given a convex function f and a set Q of probability measures, we consider the problem of minimizing the robust f -divergence infQ∈Q f(P |Q) over the class P of martingale measures. Under mild conditions on P and Q we show that a minimizer exists within the class P if limx→∞ f(x)/x =∞. If limx→∞ f(x)/x = 0 then there is a minimizer in a class P of extended martingale measures defined on the predictable σ-field. We also explain how both cases are connected to recent developments in the theory of optimal portfolio choice, in particular to robust extensions of the classical expected utility criterion.

Pessimistic Portfolio Allocation and Choquet Expected Utility

Recent developments in the theory of choice under uncertainty and risk yield a pessimistic decision theory that replaces the classical expected utility criterion with a Choquet expectation that accentuates the likelihood of the least favorable outcomes. A parallel theory has recently emerged in the literature on risk assessment. It is shown that a general form of pessimistic portfolio optimization based on the Choquet approach may be formulated as a problem of linear quantile regression. Copyright 2004, Oxford University Press.

Economic Properties of the Risk Sensitive Criterion for Portfolio Management

The idea of using stochastic control methods for theoretical studies of portfolio management has long been standard, with maximum expected utility criteria commonly being used. But in recent years a new kind of criterion, the risk sensitive criterion, has emerged from the control theory literature and been applied to portfolio management. This paper studies various economic properties of this criterion for portfolio management, thereby providing justification for its theoretical and practical use. In particular, it is shown that the risk sensitive criterion amounts to maximizing a portfolio's risk adjusted growth rate. In other words, it is essentially the same as what is commonly done in practice: find the best trade‐off between a portfolio's average return and its average volatility.

La gestion des risques environnementaux en présence d'incertitudes et de controverses scientifiques

<titre>R&#233;sum&#233;</titre> Dans cet article, nous r&#233;examinons les probl&#232;mes li&#233;s &#224; la gestion des risques environnementaux en r&#233;affirmant la distinction entre risque et incertitude introduite par Knight [1921]. La prise en compte formelle de cette incertitude est pleinement justifi&#233;e pour l&#8217;analyse des probl&#232;mes environnementaux qui sont souvent caract&#233;ris&#233;s par une absence de certitudes scientifiques. De plus, elle nous permet de rendre compte d&#8217;un certain nombre de caract&#233;ristiques essentielles de la prise de d&#233;cision dans le domaine de l&#8217;environnement que sont la controverse scientifique, les conflits entre les acteurs et les difficult&#233;s &#224; prendre des d&#233;cisions &#224; la mesure des enjeux. Enfin, la reconnaissance du r&#244;le essentiel de l&#8217;incertitude nous permet d&#8217;&#233;laborer un cadre d&#8217;analyse dans lequel nous proposons une interpr&#233;tation &#233;conomique du principe de pr&#233;caution. Nous donnons alors une justification &#224; l&#8217;adoption du crit&#232;re du maximum d&#8217;esp&#233;rance d&#8217;utilit&#233; minimum pour prendre des d&#233;cisions conformes au principe de pr&#233;caution.

Utility based pricing of contingent claims in incomplete markets

In a discrete setting, a model is developed for pricing a contingent claim in incomplete markets. Since hedging opportunities influence the price of a contingent claim, the optimal hedging strategy is first introduced assuming that a contingent claim has been issued: a strategy implemented by investing initial wealth plus the selling price is optimal if it maximizes the expected utility of the agent's net payoff, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. The ‘reservation price’ is then introduced as a subjective valuation of a contingent claim. This is defined as the minimum price that makes the issue of the claim preferable to staying put given that, once the claim has been written, the writer hedges it according to the expected utility criterion. The reservation price is defined both for a short position (reservation selling price) and for a long position (reservation buying price) in the claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu (or Black-Scholes) price. If the claim is non-redundant, then the reservation prices are interior points of the bid-ask interval. Two numerical examples are provided with different utility functions and contingent claims. Some qualitative properties of the reservation price are shown.

Exploration of the role of expectations in foreign exchange risk management

Stochastic dominance and expected utility criteria are used to explore the effects of unique expectations on foreign exchange investors. This paper illustrates the use of stochastic dominance and expected utility in selecting appropriate hedging strategies, when an individual investor's expectations of the future do not match the expectations implied in market prices. The investor is assumed to hold one unit of foreign currency. This position can be hedged by selling futures, writing covered call options, or buying protective put options. Preferences are assessed based on the stochastic dominance criteria, as well as the expected utility criteria under asymmetric information. When the investor's expectations regarding the domestic interest rate, volatility, or both are different from those of the market, we find clear preferences regarding hedging strategies. The major finding is that different sets of expectations lead to different optimal hedging strategies. Based on the particular parameters analyzed, an investor is always better off with some form of hedging.

Why Would Nature Give Individuals Utility Functions?

Consider the possible biological origin of the expected utility criterion. On the one hand, if individuals possess a utility function stemming from the rate of production of expected offspring, they can rapidly adapt to arbitrary unknown distributions in a bandit problem. Embedding such a utility function in a simple rule of thumb involving no beliefs about probabilities leads to evolutionary optimality. On the other hand, if any rule whatever yields evolutionary optimality for all distributions, this precise utility function must be implicit, in a revealed preference sense.

Decision-theoretic foundations of qualitative possibility theory

This paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with a set of acts equipped with a complete preordering relation. Conditions on acts are given that imply a possibilistic representation of the decision-maker uncertainty. In this framework, pessimistic (i.e., uncertainty-averse) as well as optimistic attitudes can be explicitly captured. The approach thus proposes an operationally testable description of possibility theory.