
on Utility Models and Prospect Theory 
By:  Mikl\'os R\'asonyi; Hasanjan Sayit 
Abstract:  Obtaining utility maximizing optimal portfolios in closed form is a challenging issue when the return vector follows a more general distribution than the normal one. In this note, we give closed form expressions, in markets based on finitely many assets, for optimal portfolios that maximize the expected exponential utility when the return vector follows normal meanvariance mixture models. We then consider large financial markets based on normal meanvariance mixture models also and show that, under exponential utility, the optimal utilities based on small markets converge to the optimal utility in the large financial market. This result shows, in particular, that to reach optimal utility level investors need to diversify their portfolios to include infinitely many assets into their portfolio and with portfolios based on any set of only finitely many assets, they never be able to reach optimum level of utility. In this paper, we also consider portfolio optimization problems with more general class of utility functions and provide an easytoimplement numerical procedure for locating optimal portfolios. Especially, our approach in this part of the paper reduces a high dimensional problem in locating optimal portfolio into a three dimensional problem for a general class of utility functions. 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2208.06549&r= 
By:  Sproule, Robert 
Abstract:  Twenty years ago, Peter Moffatt (2002) posed this general question: “Is Giffen behavior compatible with the axioms of consumer theory?” The present paper addresses this very same question, but only as it applies to the WoldJuréen (1953) utility function. In this paper, we demonstrate that the WoldJuréen (1953) utility function exhibits both Giffenity and compatibility with the axioms of consumer theory. Our singular interest in the WoldJuréen (1953) utility function stems from the fact that this utility function continues to be the preeminent theoretical benchmark in the study of Giffenity. 
Keywords:  WoldJuréen (1953) utility function,Slutsky decomposition,Giffen Behavior,Axioms of Consumer Theory 
JEL:  A22 A23 D11 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:esprep:263912&r= 
By:  Ferraz, Eduardo; Mantilla, César 
Abstract:  We use a threeperiod model adopting a recursive definition of consumption to explore the optimal delegation that a present self, aware that her nearfuture self is presentbiased but better informed, will make to protect her farfuture self against income shocks. The model captures the present self's tradeoff between using commitment mechanisms, restricting the nearfuture self's agency through illiquid savings, and profiting from the nearfuture self's better information about future shocks. Our main result states that agents with higher risk aversion can cover better against utility losses from timeinconsistent consumption through the commitment mechanism. Given the evidence of women being more riskaverse than men, this result provides the microfoundation for the gender gap in adopting financial commitment devices, especially among single individuals. 
Keywords:  commitment devices; dynamic inconsistency; EpsteinZin preferences; present bias 
JEL:  D11 D81 D90 G40 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:rie:riecdt:97&r= 
By:  Victor H. Aguiar (University of Western Ontario); Roberto Serrano (Brown University) 
Abstract:  The Slutsky matrix function encodes all the information about local variations in demand with respect to small (Slutsky) compensated price changes. When the demand function is the result of utility maximization the Slutsky matrix is symmetric. However, symmetry does not imply rationality. Here, we provide a necessary and sufficient condition for Slutsky symmetry. The new condition requires symmetric attention to compensated pricepaths. 
Keywords:  Utility Maximization, Slutsky Matrix 
JEL:  C50 C51 C52 C91 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:uwo:uwowop:20228&r= 
By:  Daniel Bartl; Johannes Wiesel 
Abstract:  We analyze the effect of small changes in the underlying probabilistic model on the value of multiperiod stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the adapted Wasserstein distance. We prove explicit firstorder approximations for both problems. Expected utility maximization is discussed as a special case. 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2208.05656&r= 
By:  Jos\'e A. Salmer\'on; Giulia Di Nunno; Bernardo D'Auria 
Abstract:  Default risk calculus emerges naturally in a portfolio optimization problem when the risky asset is threatened with a bankruptcy. The usual stochastic control techniques do not hold in this case and some additional assumptions are generally added to achieve the optimization in a beforeandafter default context. We show how it is possible to avoid one of theses restrictive assumptions, the socalled Jacod density hypothesis, by using the framework of the forward integration. In particular, in the logarithmic utility case, in order to get the optimal portfolio the right condition it is proved to be the intensity hypothesis. We use the anticipating calculus to analyze the existence of the optimal portfolio for the logarithmic utility, and than under the assumption of existence of the optimal portfolio we prove the semimartingale decomposition of the risky asset in the filtration enlarged with the default process. 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2208.07163&r= 
By:  JeanPaul Doignon; Kota Saito 
Abstract:  The Multiple Choice Polytope (MCP) is the prediction range of a random utility model due to Block and Marschak (1960). Fishburn (1998) offers a nice survey of the findings on random utility models at the time. A complete characterization of the MCP is a remarkable achievement of Falmagne (1978). Apart for a recognition of the facets by Suck (2002), the geometric structure of the MCP was apparently not much investigated. Recently, Chang, Narita and Saito (2022) refer to the adjacency of vertices while Turansick (2022) uses a condition which we show to be equivalent to the nonadjacency of two vertices. We characterize the adjacency of vertices and the adjacency of facets. To derive a more enlightening proof of Falmagne Theorem and of Suck result, Fiorini (2004) assimilates the MCP with the flow polytope of some acyclic network. Our results on adjacencies also hold for the flow polytope of any acyclic network. In particular, they apply not only to the MCP, but also to three polytopes which DavisStober, Doignon, Fiorini, Glineur and Regenwetter (2018) introduced as extended formulations of the weak order polytope, interval order polytope and semiorder polytope (the prediction ranges of other models, see for instance Fishburn and Falmagne, 1989, and Marley and Regenwetter, 2017). 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2207.06925&r= 
By:  Pascal StAmour (University of Lausanne  School of Economics and Business Administration (HECLausanne); Swiss Finance Institute) 
Abstract:  The twin arguments of (i) protecting society's most vulnerable members (e.g. agents with preexisting medical conditions, elders) from lifethreatening complications and (ii) avoiding delicate medical triage decisions were often used to warrant the substantial reallocation of economic and health care resources during the COVID19 pandemic. These justifications raise the nontrivial arbitrage between the value of lives saved by intervention vs (i) the opportunity cost of engaged resources and vs (ii) other present or future lives affected by prioritizing a single illness. This paper solves in closed form a flexible life cycle (LC) model of consumption, leisure and health choices to characterize the shadow value of life along the (i) personspecific (age, health, labour income, wealth, preferences) and (ii) mortality riskspecific (beneficial vs detrimental, temporary vs permanent changes) dimensions. The model is calibrated to reproduce observed household LC dynamics and yields plausible outofsample life values with a qualityadjusted life year (QALY) estimates between 95 and 115K$ and a Value of Statistical Life (VSL) close to 6.0M$. It identifies symmetric willingness to pay (WTP) and to accept (WTA) compensation for oneshot beneficial vs detrimental changes in longevity. Permanent changes yield asymmetric responses with larger willingness in the gains relative to loss domain and larger selling (WTA) relative to buying (WTP) prices for longevity. Ageing lowers both the value of and responsiveness to changes in longevity via falling resources and health and marginal continuation utility of living. 
Keywords:  Value of Human Life, Value of Statistical Life, Gunpoint Value, Deterministic Longevity Value, Hicksian Compensating and Equivalent Variations, Willingness to Pay, Willingness to Accept Compensation, Mortality, Longevity, NonExpected Utility. 
JEL:  J17 D15 G11 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp2262&r= 
By:  Andreas Kleiner 
Abstract:  We study a model of delegation in which a principal takes a multidimensional action and an agent has private information about a multidimensional state of the world. The principal can design any direct mechanism, including stochastic ones. We provide necessary and sufficient conditions for an arbitrary mechanism to maximize the principal's expected payoff. We also discuss simple conditions which ensure that some convex delegation set is optimal. A key step of our analysis shows that a mechanism is incentive compatible if and only if its induced indirect utility is convex and lies below the agent's firstbest payoff. 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2208.11835&r= 
By:  Shunta Akiyama; Mitsuaki Obara; Yasushi Kawase 
Abstract:  A lottery is a popular form of gambling between a seller and multiple buyers, and its profitable design is of primary interest to the seller. Designing a lottery requires modeling the buyer decisionmaking process for uncertain outcomes. One of the most promising descriptive models of such decisionmaking is the cumulative prospect theory (CPT), which represents people's different attitudes towards gain and loss, and their overestimation of extreme events. In this study, we design a lottery that maximizes the seller's profit when the buyers follow CPT. The derived problem is nonconvex and constrained, and hence, it is challenging to directly characterize its optimal solution. We overcome this difficulty by reformulating the problem as a threelevel optimization problem. The reformulation enables us to characterize the optimal solution. Based on this characterization, we propose an algorithm that computes the optimal lottery in linear time with respect to the number of lottery tickets. In addition, we provide an efficient algorithm for a more general setting in which the ticket price is constrained. To the best of the authors' knowledge, this is the first study that employs the CPT framework for designing an optimal lottery. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2209.00822&r= 
By:  Foellmi, Reto 
Abstract:  This paper studies voter turnout in concurrent votes. We develop a theoretical model that incorporates proposition salience and two types of voting costs. The first type is fixed costs of going to the polls that are to be paid only once per voting day. The second type is information costs that must be paid for each vote separately. Our model explains how the net benefit of concurrent votes, defined as salience minus information costs, enters a voter's utility function and thereby affects turnout. We test our model predictions using data on concurrent propositions in Switzerland from 19812016. Our results suggest that both the proposition with the highest net benefit and the sum of the net benefits of all concurrent propositions are important determinants of the individual turnout decision. We also find that the marginal impact on turnout rises with the net benefit of a proposition. 
Keywords:  Concurrent votes, turnout, rational voter model, referendums 
JEL:  D72 D90 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:usg:econwp:2022:09&r= 
By:  Ellingsen, Tore (Department of Economics, Stockholm School of Economics); Mohlin, Erik (Department of Economics, Lund University) 
Abstract:  We develop a formal model of social duties. Duties to respect entitlements (duties of justice) differ from duties to promote wellbeing (duties of charity). A situation specific version of our model takes entitlements as primitives. A fully portable ver sion derives entitlements from situational characteristics. Utility functions obtain kinks where duties of justice and charity are exactly satisfied. Actions at these kinks are candidates for descriptive social norms. Empirically, duties are identified using KrupkaWeber appropriateness ratings, with negative ratings indicating entitlement violations. The model’s predictions are confronted with established regularities and new survey evidence in seven preregistered applications. 
Keywords:  Social norms; Social morality; Entitlements; Dutifulness; Charity 
JEL:  D91 Z13 
Date:  2022–08–24 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2022_014&r= 
By:  Douadia Bougherara (CEEM  Centre d'Economie de l'Environnement  Montpellier  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement  Institut Agro Montpellier  Institut Agro  Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement  UM  Université de Montpellier); Lana Friesen (University of Queensland [Brisbane]); Céline Nauges (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  We study the interaction between risktaking and skewnessseeking behavior among a demographically diverse sample of French adults using an experiment that elicits certainty equivalent over lotteries that vary the second and third moments orthogonally. We find that the most common behavior is risk avoidance and skewness seeking. On average, we find no interaction between the two, and a weakly significant interaction only in some segments of the population. That is, in most cases, skewness seeking is not affected by the variance of the lotteries involved, nor is risk taking affected by the skewness of the lotteries. We also find a significant positive correlation between riskavoiding and skewnessseeking behavior. Older and female participants make more riskavoiding and more skewnessseeking choices, while less educated people and those not in executive occupations are more skewness seeking. Estimated decision models show that utility curvature, likelihood sensitivity, and optimism can explain the observed behaviors. 
Keywords:  Risk,Skewness,Certainty Equivalent,Experiment 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03739823&r= 
By:  Johanna Etner (EconomiX  UPN  Université Paris Nanterre  CNRS  Centre National de la Recherche Scientifique); Josselin Thuilliez (CES  Centre d'économie de la Sorbonne  UP1  Université Paris 1 PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Hippolyte d'Albis (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE  Paris Jourdan Sciences Economiques  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  We provide one of the first formalizations of a vaccination campaign in a decisiontheoretic framework. We analyse a model where an ambiguityaverse individual must decide how much effort to invest into prevention in the context of a rampant disease. We study how ambiguity aversion affects the effort and the estimation of the vaccine efficacy in clinical trials and immunization campaigns. We find that the behaviours of individuals participating in a clinical trial differ from individuals not participating. Individuals who are more optimistic toward vaccination participate more in trials. Their behaviours and efforts are also affected. As a result, because vaccine efficacy depends on unobserved behaviours and efforts, the biological effect of the vaccine becomes difficult to evaluate. During the scaleup phase of a vaccination campaign, provided that vaccine efficacy is established, we show that vaccine hesitancy may still be rational. 
Keywords:  Decision Theory,Vaccination,Clinical Trials,Immunization Campaigns Decision Theory,Immunization Campaigns 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:halshs03763363&r= 
By:  Imke C. Reimers; Joel Waldfogel 
Abstract:  Libraries have traditionally provided free communal access to books, facilitated by the first sale doctrine's (FSD) guarantee that libraries may purchase physical books at consumer prices. Increasingly restrictive ebook access terms may imperil libraries, and we compare the welfare cost of higher ebook prices to the welfare benefit of the FSD's guarantee of low physical book prices for libraries and their patrons. Using data on over 8,000 library systems for 20132019, we measure the impacts of physical and electronic holdings on the respective formats' circulation. We then build a structural model of the library market, and we rationalize the status quo book holdings with a librarian utility function that attaches higher weights to electronic circulation. While higher counterfactual ebook prices would induce libraries to substitute physical for electronic holdings, this would have little effect on patron CS because of consumer willingness to substitute. By contrast, higher physical book prices, as would prevail absent the first sale doctrine, reduce CS by almost ten times as much as an analogous ebook price increase. 
JEL:  H42 L82 O34 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:30392&r= 
By:  Bergeot, J.; 
Abstract:  Do children cooperate when they decide to provide informal care to their elderly parent? This paper assesses which model drives the caregiving decisions of children. I compare the predictive power of two models: a (jointutility) cooperative and a Nash noncooperative model. I focus on families with two children and one single parent. e model allows caregiving by one child to have a direct externality on the wellbeing of the sibling. The results suggest that the cooperative model overestimates the level of care received by the parents observed in the data and its predictive power is outperformed by the noncooperative model. is suggests that children are more likely to behave according to a noncooperative model. I also find that childrenâ€™s participation in caregiving has a positive externality on the wellbeing of the sibling. I construct an indicator of the degree of noncooperativeness between children and show that it is positively correlated with the number of unmet needs the parent has. I conclude that, because children do not internalize the positive externality when they behave noncooperatively, the current level of informal care provided to parents appears to suffer from a public good problem. 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:yor:hectdg:22/13&r= 
By:  Ioan Alexandru Puiu; Raphael Andreas Hauser 
Abstract:  Spot electricity markets are considered under a GameTheoretic framework, where risk averse players submit orders to the market clearing mechanism to maximise their own utility. Consistent with the current practice in Europe, the market clearing mechanism is modelled as a Social Welfare Maximisation problem, with zonal pricing, and we consider inflexible demand, physical constraints of the electricity grid, and capacityconstrained producers. A novel type of nonparametric risk aversion based on a defined worst case scenario is introduced, and this reduces the dimensionality of the strategy variables and ensures boundedness of prices. By leveraging these properties we devise Jacobi and GaussSeidel iterative schemes for computation of approximate global Nash Equilibria, which are in contrast to derivative based local equilibria. Our methodology is applied to the real world data of Central Western European (CWE) Spot Market during the 20192020 period, and offers a good representation of the historical time series of prices. By also solving for the assumption of truthful bidding, we devise a simple method based on hypothesis testing to infer if and when producers are bidding strategically (instead of truthfully), and we find evidence suggesting that strategic bidding may be fairly pronounced in the CWE region. 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2208.14164&r= 
By:  Meena Jagadeesan; Michael I. Jordan; Nika Haghtalab 
Abstract:  Competition between traditional platforms is known to improve user utility by aligning the platform's actions with user preferences. But to what extent is alignment exhibited in datadriven marketplaces? To study this question from a theoretical perspective, we introduce a duopoly market where platform actions are bandit algorithms and the two platforms compete for user participation. A salient feature of this market is that the quality of recommendations depends on both the bandit algorithm and the amount of data provided by interactions from users. This interdependency between the algorithm performance and the actions of users complicates the structure of market equilibria and their quality in terms of user utility. Our main finding is that competition in this market does not perfectly align market outcomes with user utility. Interestingly, market outcomes exhibit misalignment not only when the platforms have separate data repositories, but also when the platforms have a shared data repository. Nonetheless, the data sharing assumptions impact what mechanism drives misalignment and also affect the specific form of misalignment (e.g. the quality of the bestcase and worstcase market outcomes). More broadly, our work illustrates that competition in digital marketplaces has subtle consequences for user utility that merit further investigation. 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2208.14423&r= 
By:  Franz Ostrizek; Denis Shishkin 
Abstract:  We study a decisionframing design problem: a principal faces an agent with framedependent preferences and designs an extensive form with a frame at each stage. This allows the principal to circumvent incentive compatibility constraints by inducing dynamically inconsistent choices of the sophisticated agent. We show that a vector of contracts can be implemented if and only if it can be implemented using a canonical extensive form, which has a simple highlowhigh structure using only three stages and the two highest frames, and employs unchosen decoy contracts to deter deviations. We then turn to the study of optimal contracts in the context of the classic monopolistic screening problem and establish the existence of a canonical optimal mechanism, even though our implementability result does not directly apply. In the presence of naive types, the principal can perfectly screen by cognitive type and extract full surplus from naifs. 
Keywords:  Implementation, Screening, Framing, ExtensiveForm Decision Problems, Dynamic Inconsistency, Sophistication, Naivete 
JEL:  D42 D82 D90 L12 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_364&r= 
By:  Keisuke Kizaki (Faculty of Economics, The University of Tokyo); Taiga Saito (Faculty of Economics, The University of Tokyo); Akihiko Takahashi (Faculty of Economics, The University of Tokyo) 
Abstract:  This paper considers a multiagent optimal investment problem with conservative sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative sentiments of the agents by a supinf/infsup problem where we take infimum on a choice of a probability measure and supremum on trading strategies. To the best of our knowledge, this is the first attempt to investigate a multiagent equilibrium model in an incomplete setting with heterogeneous views on Brownian motions. Moreover, we show two cases where the trading strategies and the excess return process of the risky asset in equilibrium are explicitly solved. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under conservative sentiments, which explain how the sentiments affect the trading strategies of the agents and the expected return process of the risky asset. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2022cf1198&r= 