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on Utility Models and Prospect Theory |
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Issue of 2022‒01‒17
twelve papers chosen by |
| By: | Nail Kashaev; Victor Aguiar |
| Abstract: | We present a novel characterization of random rank-dependent expected utility for finite datasets and finite prizes. The test lends itself to statistical testing using the tools in Kitamura and Stoye (2018). |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.13649&r= |
| By: | Martin Herdegen; David Hobson; Joseph Jerome |
| Abstract: | In this article, we consider the optimal investment-consumption problem for an agent with preferences governed by Epstein--Zin stochastic differential utility (EZ-SDU) who invests in a constant-parameter Black-Scholes-Merton market over the infinite horizon. The parameter combinations that we consider in this paper are such that the risk aversion parameter $R$ and the elasticity of intertemporal complementarity $S$ satisfy $\theta=\frac{1-R}{1-S}>1$. In this sense, this paper is complementary to Herdegen, Hobson and Jerome [arXiv:2107.06593]. The main novelty of the case $\theta>1$ (as opposed to $\theta\in(0,1)$) is that there is an infinite family of utility processes associated to every nonzero consumption stream. To deal with this issue, we introduce the economically motivated notion of a proper utility process, where, roughly speaking, a utility process is proper if it is nonzero whenever future consumption is nonzero. We then proceed to show that for a very wide class of consumption streams $C$, there exists a proper utility process $V$ associated to $C$. Furthermore, for a wide class of consumption streams $C$, the proper utility process $V$ is unique. Finally, we solve the optimal investment-consumption problem in a constant parameter financial market, where we optimise over the right-continuous attainable consumption streams that have a unique proper utility process associated to them. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.06708&r= |
| By: | V. I. Yukalov |
| Abstract: | The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to resolve it have considered some variants of the original set-up, but the original paradox has remained unresolved, while the proposed variants have introduced new complications and problems. Here a rigorous mathematical resolution of the St. Petersburg paradox is suggested based on a probabilistic approach to decision theory. |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2111.14635&r= |
| By: | Walter Briec |
| Abstract: | This paper defines a new distance function in production theory that generalizes several existing efficiency measures. The new distance function is inspired from the Atkinson inequality index and maximizes the generalized sum of netput expansions until an efficient point is reached. Along this line, many measures of technical efficiency are derived from the maximization of a utility function built on the Stone-Geary model. In particular, the directional distance function is expressed from the maximization of a suitable Leontief utility function. A generalized mean duality theorem is proven and a dual correspondence is developed between the generalized directional distance function and the profit function. It is then shown that, for every feasible production vectors, all previous dual correspondences are special cases of this correspondence. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.09443&r= |
| By: | Kasberger, Bernhard; Woodward, Kyle |
| Abstract: | We study multi-unit auctions in which bidders have limited knowledge of opponent strategies and values. We characterize optimal prior-free bids; these bids minimize the maximal loss in expected utility resulting from uncertainty surrounding opponent behavior. Optimal bids are simply computable despite bidders having multi-dimensional private information, and in certain cases admit closed-form solutions. In the pay-as-bid auction the minimax-loss bid is unique; in the uniform-price auction the minimax-loss bid is unique if the bidder is allowed to determine the quantities for which they bid, as in many practical applications. Payments to the seller may be higher in either auction format, but minimax-loss bids are never uniformly higher in the pay-as-bid auction. |
| Keywords: | Auctions; multi-unit auctions; loss minimization; non-Bayesian approaches |
| JEL: | D44 D81 |
| Date: | 2021–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111185&r= |
| By: | Thomas Epper (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique, IÉSEG School Of Management [Puteaux]); Helga Fehr-Duda (University of Zurich, Department of Banking and Finance) |
| Abstract: | Standard economic models view risk taking and time discounting as two independent dimensions of decision making. However, mounting experimental evidence demonstrates striking parallels in patterns of risk taking and time discounting behavior and systematic interaction effects, which suggests that there may be common underlying forces driving these interactions. Here we show that the inherent uncertainty associated with future prospects together with individuals' proneness to probability weighting generates a unifying framework for explaining a large number of puzzling behavioral regularities: delay-dependent risk tolerance, aversion to sequential resolution of uncertainty, preferences for the timing of the resolution of uncertainty, the differential discounting of risky and certain outcomes, hyperbolic discounting, subadditive discounting, and the order dependence of prospect valuation. Furthermore, all these phenomena can be predicted simultaneously with the same set of preference parameters. |
| Keywords: | risk preferences,time preferences,preference interaction,increasing risk tolerance |
| Date: | 2021–12–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03473431&r= |
| By: | Christoph Heinzel (SMART-LERECO - Structures et Marché Agricoles, Ressources et Territoires - AGROCAMPUS OUEST - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Richard Peter (University of Iowa) |
| Abstract: | Using a unified approach, we show how precautionary saving, self-protection and self-insurance are jointly determined by risk preferences and the preference over the timing of uncertainty resolution. We cover higher-order risk effects and examine both risk averters and risk lovers. When decision-makers use several instruments simultaneously to respond to income risk, substitutive interaction effects arise. We quantify precautionary and substitution effects numerically and discuss the role of instrument interaction for the inference of preference parameters from precautionary motives. Instruments can differ substantially in the size of the precautionary motive and in the susceptibility to substitution effects. This affects their suitability for the identification of precautionary preferences. |
| Abstract: | En utilisant une approche unifiée, nous montrons comment les choix de précaution de l'épargne, l'auto-protection et l'auto-assurance sont simultanément déterminés par les préférences face au risque et la préférence pour le moment de la résolution d'incertitude. Nous tenons compte des effets de risque d'ordre élevé et considérons l'aversion face au risque, ainsi que le goût pour le risque. Des effets d'interaction substitutifs se produisent si les décideurs se servent de plusieurs instruments à la fois pour répondre à un risque exogène sur le revenu. Nous quantifions de manière numérique les effets de précaution et de substitution. Nous discutons le rôle de l'interaction entre les instruments pour la détermination des paramètres de préférences à partir des motifs de précaution. Les instruments diffèrent de manière substantielle par rapport à la taille du motif de précaution, ainsi que leur susceptibilité à des effets d'interaction. Ces différences affectent le degré auquel les instruments pourront contribuer à l'identification des préférences pour la précaution. |
| Keywords: | Recursive preferences,Prudence,Precautionary behavior,Interaction effects,Comparative statics,Préférences récursives,Comportement de précaution,Effets d’interaction,Statique comparative |
| Date: | 2021–12–17 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03484875&r= |
| By: | Polterovich, Victor; Ilinskiy, Dmitry |
| Abstract: | We propose a model of a firm that differentiates prices for finished and unfinished housing. The demand for housing is formed by consumers solving a dynamic utility maximization problem. The proposed formulation of this problem takes into account the fact that the purchased apartment may be available for consumption only after a certain time. In this case, at the moment of receiving the ready-made apartment the consumer gets rid of the need to pay the rent for the apartment in which he previously lived. Numerical calculations based on the data typical for the Moscow housing market have shown that relatively poor segments of the population prefer to pay for the apartment when it is not ready. At the same time the lower the rent rate, the higher the price of unfinished apartments and the relatively lower the share of consumers who prefer to buy them |
| Keywords: | price of unfinished apartment, housing rent, loan rate, developer's profit |
| JEL: | D02 D14 G21 |
| Date: | 2021–12–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:110947&r= |
| By: | Demeze-Jouatsa, Ghislain-Herman (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Call a mechanism that associates each profile of preferences over candidates to an ambiguous act an Ambiguous Social Function (ASCF). This paper studies the strategy-proofness of ASCFs. We find that an ASCF is unanimous and strategyproof if and only if there exists a nonempty subset of voters, called the set of top voters, such that at each preference profile, the range of the selected act equals the set of top-ranked candidates of top voters. We provide a full characterization of the class of unanimous, strategyproof, and anonymous ASCFs, and provide a large subclass of ASCFs that satisfy the additional property of neutrality. |
| Keywords: | Social Choice Function, Ambiguity Aversion, Ellsberg Urns, Strategy-proofness, Unanimity, Anonymity, Neutrality |
| Date: | 2022–01–07 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:660&r= |
| By: | Ling Wang; Kexin Chen; Mei Choi Chiu; Hoi Ying Wong |
| Abstract: | Any firm whose business strategy has an exposure constraint that limits its potential gain naturally considers expansion, as this can increase its exposure. We model business expansion as an enlargement of the opportunity set for business policies. However, expansion is irreversible and has an opportunity cost attached. We use the expected optimization of utility to formulate this as a novel stochastic control problem combined with an optimal stopping time, and we derive an explicit solution for exponential utility. We apply the framework to an investment and a reinsurance scenario. In the investment problem, the cost and incentives to increase the trading exposure are analyzed, while the optimal timing for an insurer to launch its reinsurance business is investigated in the reinsurance problem. Our model predicts that the additional income gained through business expansion is the key incentive for a decision to expand. Interestingly, companies may have this incentive but are likely to wait for a period of time before expanding, although situations of zero opportunity cost or specific restrictive conditions on the model parameters are exceptions to waiting. The business policy remains on the boundary of the opportunity set before expansion during the waiting period. The length of the waiting period is related to the opportunity cost, return, and risk of the expanded business. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.06706&r= |
| By: | Pengcheng You; Yan Jiang; Enoch Yeung; Dennice F. Gayme; Enrique Mallada |
| Abstract: | This paper focuses on the operation of an electricity market that accounts for participants that bid at a sub-minute timescale. To that end, we model the market-clearing process as a dynamical system, called market dynamics, which is temporally coupled with the grid frequency dynamics and is thus required to guarantee system-wide stability while meeting the system operational constraints. We characterize participants as price-takers who rationally update their bids to maximize their utility in response to real-time schedules of prices and dispatch. For two common bidding mechanisms, based on quantity and price, we identify a notion of alignment between participants' behavior and planners' goals that leads to a saddle-based design of the market that guarantees convergence to a point meeting all operational constraints. We further explore cases where this alignment property does not hold and observe that misaligned participants' bidding can destabilize the closed-loop system. We thus design a regularized version of the market dynamics that recovers all the desirable stability and steady-state performance guarantees. Numerical tests validate our results on the IEEE 39-bus system. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.05811&r= |
| By: | Garzarelli, Giampaolo; Keeton, Lyndal; Sitoe, Aldo A. |
| Abstract: | What is the tenet upon which the public policy of lockdown by fiat experienced during the COVID-19 pandemic is based on? The work approaches this question about the rationale of the mandatory shelter-in-place policy as an interpersonal exchange of rights, but where the exchange occurs coercively instead of voluntarily. It compares, in positive political economy terms, the normative principles of utilitarianism and Rawlsianism, and shows that lockdown by fiat is a policy that is closer to a maximin equity criterion rather than to a utilitarian one. The work moreover shows, also with the aid of a thought experiment in the spirit of Rawls and with factual applications, that the fiat redistribution of rights to liberty in favor of rights to health – from those least affected to those most affected by COVID-19 – is, in the main, a policy choice that is to be expected under certain constraints. |
| Keywords: | Covid-19 pandemic,Health rights,Liberty,Public policy,Lockdown,Rawls |
| JEL: | D04 D78 H11 H12 I18 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:esprep:248469&r= |