|
on Utility Models and Prospect Theory |
|
Issue of 2021‒01‒25
twenty papers chosen by |
| By: | Seiji TAKANASHI |
| Abstract: | We extend the domain of social preferences, which depend on not only one’s outcomes but also vectors of outcomes of all other agents, from deterministic outcome vectors to lotteries over outcome vectors. First, we axiomatically characterize a class of utility functions which satisfies the expected utility theory and reversal of order as far as these two requirements are consistent with ex post fairness and ex ante fairness. Based on this class, we characterize three classes of utility functions which additionally satisfy ex ante fairness, inequality-aversion, and ex post fairness for probability mixture, respectively. Finally, we characterize our main class of utility functions which satisfies these axioms. Saito (2013) also axiomatizes social preferences on lotteries over the outcome vectors which are an extension of the utility functions proposed by Fehr and Schmidt (1999). We characterize a wider class of utility functions which explains heterogeneous attitudes of how much the decision maker cares about ex ante fairness and ex post fairness toward each agent. Moreover, we provide an additional axiom under which our class of utility functions coincides with Saito’s class of utility functions. We reveal that the axiom requires that the attitudes are the same among all the agents. |
| Keywords: | Social preference, Risk, Fairness |
| JEL: | D81 D63 D91 |
| URL: | http://d.repec.org/n?u=RePEc:kue:epaper:e-20-006&r=all |
| By: | Antoine Bommier (ETH Zurich); Daniel Harenberg (ETH Zurich); François Le Grand (EMLyon Business School); Cormac O'Dea (Cowles Foundation, Yale University) |
| Abstract: | We analyze lifecycle saving strategies using a recursive utility model calibrated to match empirical estimates of the value of a statistical life. The novelty of our approach is that we require preferences to be monotone with respect to ï¬ rst order stochastic dominance. The framework we use can disentangle risk aversion and the intertemporal elasticity and can feature a positive value of life without placing constraints on the value of the risk aversion parameter or the intertemporal elasticity of substitution. We show that, with a positive value of life, risk aversion reduces savings, decreases stock market participation and decreases annuity purchase. Risk averse agents are willing to make an early death a not-so-adverse outcome by enjoying greater consumption when young and bequeathing wealth in case of death. The model can rationalize low annuity demand while also matching empirically documented levels of wealth and private investments in stocks. |
| Keywords: | Lifecycle model, Value of life, Risk aversion, Saving choices, Portfolio choices, Annuity puzzle, Recursive utility |
| JEL: | D91 G11 J14 J17 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2231r&r=all |
| By: | Yosuke Hashidate; Keisuke Yoshihara |
| Abstract: | In this paper, we propose a theory to identify the motivations behind altruistic or prosocial behavior. We focus on inequity aversion and shame aversion as social image concerns. To study these, we characterize two additively perturbed utility models, that is, the sum of expected utility and a non-linear cost function. First, we examine how to distinguish between stochastic inequity-averse behavior and stochastic shame-averse behavior. Next, we show that additively perturbed inequity-averse utility captures the general class of inequity-averse preferences, including ex-ante and ex-post fairness. Finally, we consider the relationship between our models and random utility, one of the most common stochastic choice models. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:tcr:wpaper:e155&r=all |
| By: | Andersson, Tommy (Department of Economics, Lund University); Ehlers, Lars (Département de sciences économiques, Université de Montréal) |
| Abstract: | We analyze the problem of allocating indivisible objects and monetary compensations to a set of agents. In particular, we consider envy-free and budget-balanced rules that are least manipulable with respect to agents counting or with respect to utility gains. A key observation is that, for any profile of quasi-linear preferences, the outcome of any such least manipulable envy-free rule can be obtained via so-called agent-k-linked allocations. Given this observation, we provide an algorithm for identifying agent-k-linked allocations. |
| Keywords: | Envy-freeness; Budget-balance; Least manipulable; Algorithm |
| JEL: | C71 C78 D63 D71 D78 |
| Date: | 2021–01–14 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2021_002&r=all |
| By: | Mahan Tahvildari |
| Abstract: | We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market, often called a basis risk model. The market agent's risk preferences are modelled using a so-called forward performance process (forward utility), which is a time-decreasing utility of exponential type. Moreover, the market agent (investor) does not know with certainty the values of the asset price drifts. This market setting with drift parameter uncertainty is the partial information scenario. We discuss the stochastic control problem obtained by setting up the hedging portfolio and derive the optimal hedging strategy. Furthermore, a (dual) forward indifference price representation of the claim and its PDE are obtained. With these results, the residual risk process representing the basis risk (hedging error), pay-off decompositions and asymptotic expansions of the indifference price in the European case are derived. We develop the analogous stochastic control and stopping problem with an American claim and obtain the corresponding forward indifference price valuation formula. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.00251&r=all |
| By: | Zhuo Jin; Zuo Quan Xu; Bin Zou |
| Abstract: | We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expected utility of dividend payments over an infinite horizon. By applying a perturbation approach, we obtain the optimal strategy and the value function in closed form for log and power utility. We conduct an economic analysis to investigate the impact of various model parameters and risk aversion on the insurer's optimal strategy. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.06703&r=all |
| By: | Margherita Borella; Mariacristina De Nardi |
| Abstract: | In old age, consumption can fluctuate because of shocks to available resources and because health shocks affect utility from consumption. We find that even temporary drops in income and health are associated with drops in consumption and most of the effect of temporary drops in health on consumption stems from the reduction in the marginal utility from consumption that they generate. More precisely, after a health shock, richer households adjust their consumption of luxury goods because their utility of consuming them changes. Poorer households, instead, adjust both their necessary and luxury consumption because of changing resources and utility from consumption. |
| JEL: | D10 D11 D12 D14 E20 E21 H20 H31 H51 |
| Date: | 2020–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedmoi:89237&r=all |
| By: | Venegas-Martínez, Francisco |
| Abstract: | RESUMEN Esta investigación con base en la teoría del consumidor racional da respuesta a la siguiente pregunta: ¿Qué condiciones debe satisfacer una ecuación diferencial de primer orden no homogénea con condiciones inicial y final para que tenga una única solución? Para ello, se desarrolla un problema de un consumidor racional que maximiza utilidad total descontada (con su tasa de descuento subjetiva) sobre un bien de consumo no perecedero, en tiempo continuo y en un horizonte de planeación finito, sujeto a que el valor presente descontado (con la tasa de interés real) del consumo planeado sea igual a su riqueza inicial (positiva) y que no deja herencia. ABSTRACT This investigation based on the theory of the rational consumer answers the following question: What condition must a inhomogeneous first-order differential equation with initial and final conditions satisfy to have a unique solution? To do this, a problem of a rational consumer that maximizes his total discounted utility (with his subjective discount rate) on a non-perishable consumer good, in continuous time in a finite planning horizon, subject to the discounted present value (with the real interest rate) of his planned consumption is equal to his initial (positive) wealth and does not leave inheritance. |
| Keywords: | métodos matemáticos, ecuaciones diferenciales parciales, consumidor racional mathematical methods, partial differential equations, rational consumer. |
| JEL: | C61 |
| Date: | 2021–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:105134&r=all |
| By: | Loïc Berger (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]); Louis Eeckhoudt (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) |
| Abstract: | Diversification is a basic economic principle that helps to hedge against uncertainty. It is therefore intuitive that both risk aversion and ambiguity aversion should positively affect the value of diversification. In this paper, we show that this intuition (1) is true for risk aversion but (2) is not necessarily true for ambiguity aversion. We derive sufficient conditions, showing that, contrary to the economic intuition, ambiguity and ambiguity aversion may actually reduce the diversification value. |
| Keywords: | Diversification,ambiguity aversion,model uncertainty,hedging |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-02910906&r=all |
| By: | Szwagrzak, Karol (Department of Economics, Copenhagen Business School) |
| Abstract: | We model how sample evidence guides choice: An agent faces a number of alternative actions. For each action, she observes a sample of outcomes; she cannot see the distribution from where the sample was drawn. To make her choice, she evaluates the evidence for the hypothesis that an action is optimal. The strength of evidence in favor of the hypothesis is measured by the average decision utility of the outcomes in its sample; its weight gauges predictive validity and is approximated by the size of the sample. We identify necessary and sufficient conditions for her choice to be determined by the interaction of strength and weight, reflecting the determinants of confidence judgements documented in experiments (Griffin and Tversky, 1992). These conditions characterize a model consistent with non-trivial uncertainty attitudes and “frequentist" expected utility maximization. |
| Keywords: | Sample; Sample size; Uncertainty attitudes |
| JEL: | D81 D83 |
| Date: | 2021–01–08 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:cbsnow:2021_003&r=all |
| By: | Ram S. Dubey; Giorgio Laguzzi |
| Abstract: | We propose generalized versions of strong equity and Pigou-Dalton transfer principle. We study the existence and the real valued representation of social welfare relations satisfying these two generalized equity principles. Our results characterize the restrictions on one period utility domains for the equitable social welfare relation (i) to exist; and (ii) to admit real-valued representations. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.06481&r=all |
| By: | Matteo Brachetta; Claudia Ceci |
| Abstract: | We investigate an optimal reinsurance problem for an insurance company facing a constant fixed cost when the reinsurance contract is signed. The insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level in order to maximize the expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cram\'er-Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.04975&r=all |
| By: | Jin Xi; Haitian Xie |
| Abstract: | This paper studies the robust mechanism design problem of a public good when there are many agents. We propose a class of dominant strategy incentive compatible (DSIC) and ex post individual rational (EPIR) mechanisms that balance the budget and approximates the first-best welfare level when the number of participants is large. The decision rule is based on thresholding the sum of transformed valuations of the agents. We show that the rate of change of the threshold is the key to characterizing the trade-off between balancing the budget and maximizing the welfare. In particular, we find that when this rate is controlled in a certain range, the two goals can be achieved at the same time asymptotically. The proposed mechanisms are robust in two ways: first, they depend on the valuation distributions only through certain moments; second, they allow for asymmetric and irregular valuation distributions. More specifically, we show that the Myerson regularity condition plays no role in this constrained problem of welfare approximation. In addition to welfare approximation, we also study profit approximation using similar mechanisms but with a different threshold and show that a fraction of the optimal profit can be achieved with a large number of participants. Lastly, we extend the model to accommodate for non-binary decision and general utility functions. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.02423&r=all |
| By: | Soham R. Phade; Venkat Anantharam |
| Abstract: | This paper initiates a discussion of mechanism design when the participating agents exhibit preferences that deviate from expected utility theory (EUT). In particular, we consider mechanism design for systems where the agents are modeled as having cumulative prospect theory (CPT) preferences, which is a generalization of EUT preferences. We point out some of the key modifications needed in the theory of mechanism design that arise from agents having CPT preferences and some of the shortcomings of the classical mechanism design framework. In particular, we show that the revelation principle, which has traditionally played a fundamental role in mechanism design, does not continue to hold under CPT. We develop an appropriate framework that we call mediated mechanism design which allows us to recover the revelation principle for CPT agents. We conclude with some interesting directions for future work. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.08722&r=all |
| By: | Jianming Xia |
| Abstract: | In this paper we characterize the niveloidal preferences that satisfy the Weak Order, Monotonicity, Archimedean, and Weak C-Independence Axioms from the point of view of an intra-personal, leader-follower game. We also show that the leader's strategy space can serve as an ambiguity aversion index. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.07509&r=all |
| By: | Robin Cubitt (University of Nottingham); Orestis Kopsacheilis (Technical University of Munich); Chris Starmer (University of Nottingham) |
| Abstract: | The Description-Experience gap (DE gap) is widely thought of as a tendency for people to act as if overweighting rare events when information about those events is derived from descriptions but as if underweighting rare events when they experience them through a sampling process. While there is now clear evidence that some form of DE gap exists, its causes, exact nature and implications for economic theory remain unclear, for reasons we explain. We present a new experiment which examines in a unified design four distinct causal mechanisms that might drive the DE gap, attributing it respectively to information differences (sampling bias), to a feature of preferences (ambiguity sensitivity) or to aspects of cognition (likelihood representation and memory). Using a model-free approach, we elicit a DE gap similar in direction and size to the literature’s average and find that, when each factor is considered in isolation, sampling bias stemming from under-represented rare events is the only significant driver of the gap. Yet, model-mediated analysis reveals the possibility of a smaller DE gap, existing even without information differences. Moreover, this form of analysis of our data indicates that, even when information about them is obtained by sampling, rare events are generally overweighted. |
| Keywords: | Decisions from Description, Decisions from Experience, Risk Preferences, Cumulative Prospect Theory, Ambiguity |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2020-19&r=all |
| By: | Emmanuelle Augeraud-Véron (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique); Giorgio Fabbri (GAEL - Laboratoire d'Economie Appliquée de Grenoble - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes); Katheline Schubert (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | We study a model of strategic competition among farmers for land use in an agricultural economy. Each agent can take possession of a part of the collective forest land and convert it to farming. Unconverted forest land helps preserving biodiversity, which contributes to reducing the volatility of agricultural production. Agents' utility is given in terms of a Kreps Porteus stochastic dierential utility capable of disentangling risk aversion and aversion to uctuations. We characterize the land used by each farmer and her welfare at the Nash equilibrium, we evaluate the over-exploitation of the land and the agents' welfare loss compared to the socially optimal solution and we study the drivers of the ineciencies of the decentralized equilibrium. After characterizing the value of biodiversity in the model, we use an appropriate decomposition to study the policy implications of the model by identifying in which cases the allocation of property rights is preferable to the introduction of a land conversion tax. |
| Keywords: | Biodiversity,insurance value,land conversion,recursive preferences,stochastic dierential games Q56,Q58,Q10,Q15,O13,O20,C73,D62 |
| Date: | 2020–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-03038977&r=all |
| By: | Rosas, Francisco; Acerenza, Santiago; Orazem, Peter F. |
| Abstract: | Contingent valuation methods are used to identify observed and unobserved preferences of goods and services. We apply these methods, in the context of multivariate probit analysis, to compute willingness to pay for each product of a cluster of goods conditional on having purchased another offered good of the cluster. We also provide a derivation of compensated cross-price elasticities based on unobservable factors, proving to be convenient in situations where cross-prices are not part of the demand equations. As goods belonging to a cluster typically embed correlated taste, their pricing strategy should consider all offered goods simultaneously rather than individually. Therefore, we solve for the set of optimal prices of a social planner whose objective function weights both the producer’s revenues and the consumer’s joint latent utility. We show an application to collegiate sports events, but these methods can be extended in a straightforward fashion to other goods and services. Supplementary materials for this article are available online. |
| Date: | 2020–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:isu:genstf:202001010800001008&r=all |
| By: | Nina Biljanovska; Alexandros Vardoulakis |
| Abstract: | We study how financial frictions amplify labor supply shocks in a macroeconomic model with occasionally binding financing constraints. Workers supply labor to entrepreneurs who borrow to purchase factors of production. Borrowing capacity is restricted by the value of capital, generating a pecuniary externality when financing constraints bind. Additionally, there is a distributive externality operating through wages. The planner’s allocation can be decentralized with two instruments: a credit tax/subsidy and a labor tax/subsidy. Labor shocks, such as the COVID-19 shock, amplify the policy responses, which critically depend on whether financing constraints bind or not. |
| Keywords: | Labor supply;Collateral;Labor taxes;Supply shocks;Labor;WP,utility function,quantitative analysis |
| Date: | 2020–09–18 |
| URL: | http://d.repec.org/n?u=RePEc:imf:imfwpa:2020/189&r=all |
| By: | Francesco Fallucchi; Marc Kaufmann |
| Abstract: | Many important economic outcomes result from cumulative effects of smaller choices, so the best outcomes require accounting for other choices at each decision point. We document narrow bracketing -- the neglect of such accounting -- in work choices in a pre-registered experiment on MTurk: bracketing changes average willingness to work by 13-28%. In our experiment, broad bracketing is so simple to implement that narrow bracketing cannot possibly be due to optimal conservation of cognitive resources, so it must be suboptimal. We jointly estimate disutility of work and bracketing, finding gender differences in convexity of disutility, but not in bracketing. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2101.04529&r=all |