
on Utility Models and Prospect Theory 
Issue of 2021‒11‒29
fifteen papers chosen by 
By:  Aurelien Baillon; Yoram Halevy; Chen Li 
Abstract:  Facing several decisions, people may consider each one in isolation or integrate them into a single optimization problem. Isolation and integration may yield different choices, for instance, if uncertainty is involved, and only one randomly selected decision is implemented. We investigate whether the random incentive system in experiments that measure ambiguity aversion provides a hedge against ambiguity, making ambiguityaverse subjects who integrate behave as if they were ambiguity neutral. Our results suggest that about half of the ambiguity averse subjects integrated their choices in the experiment into a single problem, whereas the other half isolated. Our design further enable us to disentangle properties of the integrating subjects' preferences over compound objects induced by the random incentive system and the choice problems in the experiment. 
Keywords:  hedging, random incentives, Ellsberg, ambiguity aversion, design of experiments, integration, isolation, narrow bracketing, narrow framing 
JEL:  C81 C91 D81 
Date:  2021–11–15 
URL:  http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa712&r= 
By:  Blanchet, Jose H. (Stanford U); Reiman, Martin I. (Columbia U); Shah, Virag (Stanford U); Wein, Lawrence M. (Stanford U); Wu, Linjia (Stanford U) 
Abstract:  We consider a matching market where buyers and sellers arrive according to independent Poisson processes at the same rate and independently abandon the market if not matched after an exponential amount of time with the same mean. In this centralized market, the utility for the system manager from matching any buyer and any seller is a general random variable. We consider a sequence of systems indexed by n where the arrivals in the nth system are sped up by a factor of n. We analyze two families of oneparameter policies: the population threshold policy immediately matches an arriving agent to its best available mate only if the number of mates in the system is above a threshold, and the utility threshold policy matches an arriving agent to its best available mate only if the corresponding utility is above a threshold. Using an asymptotic fluid analysis of the twodimensional Markov process of buyers and sellers, we show that when the matching utility distribution is lighttailed, the population threshold policy with threshold n/ln n is asymptotically optimal among all policies that make matches only at agent arrival epochs. In the heavytailed case, we characterize the optimal threshold level for both policies. We also study the utility threshold policy in an unbalanced matching market with heavytailed matching utilities, and find that the buyers and sellers have the same asymptotically optimal utility threshold. To illustrate our theoretical results, we use extreme value theory to derive optimal thresholds when the matching utility distribution is exponential, uniform, Pareto, and correlated Pareto. In general, we find that as the right tail of the matching utility distribution gets heavier, the threshold level of each policy (and hence market thickness) increases, as does the magnitude by which the utility threshold policy outperforms the population threshold policy. 
Date:  2020–12 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:3916&r= 
By:  Eddy Keming Chen; Daniel Rubio 
Abstract:  Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.00862&r= 
By:  Thomas Dohmen; Arjan Non; Tom Stolp 
Abstract:  We conduct laboratory experiments to investigate basic predictions of principalagent theory about the choice of piece rate contracts in the presence of output risk, and provide novel insights that reference dependent preferences affect the tradeoff between risk and incentives. Subjects in our experiments choose their compensation for performing a realeffort task from a menu of linear piece rate and fixed payment combinations. As classical principalagent models predict, more risk averse individuals choose lower piece rates. However, in contrast to those predictions, we find that lowproductivity risk averse workers choose higher piece rates when the riskiness of the environment increases. We hypothesize that reference points affect piece rate choice in risky environments, such that individuals whose expected earnings would exceed (fall below) the reference point in a riskfree environment behave risk averse (seeking) in risky environments. In a second experiment, we exogenously manipulate reference points and confirm this hypothesis. 
Keywords:  Incentive, piecerate, risk, reference point, laboratory experiment 
JEL:  D81 D91 M52 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2021_322&r= 
By:  Lokka, A.; Xu, Junwei 
Abstract:  We consider an optimal liquidation problem with infinite horizon in the Almgren–Chriss framework, where the unaffected asset price follows a Lévy process. The temporary price impact is described by a general function that satisfies some reasonable conditions. We consider a market agent with constant absolute risk aversion, who wants to maximize the expected utility of the cash received from the sale of the agent’s assets, and show that this problem can be reduced to a deterministic optimization problem that we are able to solve explicitly. In order to compare our results with exponential Lévy models, which provide a very good statistical fit with observed asset price data for short time horizons, we derive the (linear) Lévy process approximation of such models. In particular we derive expressions for the Lévy process approximation of the exponential variance–gamma Lévy process, and study properties of the corresponding optimal liquidation strategy. We then provide a comparison of the liquidation trajectories for reasonable parameters between the Lévy process model and the classical Almgren–Chriss model. In particular, we obtain an explicit expression for the connection between the temporary impact function for the Lévy model and the temporary impact function for the Brownian motion model (the classical Almgren–Chriss model), for which the optimal liquidation trajectories for the two models coincide. 
Keywords:  Lévy processes; AlmgrenChriss model; algorithmic trading; optimal liquidation; optimal execution; constant absolute risk aversion; market impact; optimal control; HamiltonJacobiBellman equation 
JEL:  F3 G3 
Date:  2020–11–28 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:106977&r= 
By:  Senran Lin 
Abstract:  This paper studies the advancepurchase problem when a consumer has referencedependent preferences in the form of Koszegi and Rabin (2009), in which planning affects reference formation. When the consumer exhibits plan revisability, loss aversion increases the price at which she is willing to prepurchase. This implies that loss aversion can lead to riskseeking. Moreover, I endogenize the seller$'$s pricecommitment behavior in the advancepurchase problem. The result shows that the seller commits to his spot price even if he is not obliged to, which was treated as a given assumption in previous literature. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.14929&r= 
By:  Atilla Aras 
Abstract:  This study provides the solution to the equity premium puzzle. The new model was developed by including the behavior of investors toward risk in financial markets in prior studies. The calculations of this newly tested model show that the value of the coefficient of relative risk aversion is 1.033526 by assuming the value of the subjective time discount factor to be 0.99. Since these values are compatible with the existing empirical studies, they confirm the validity of the newly derived model that provides the solution to the equity premium puzzle. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.14405&r= 
By:  Aurelien Baillon; Yoram Halevy; Chen Li 
Abstract:  We demonstrate how the standard usage of the random incentive system in ambiguity experiments eliciting certainty and probability equivalents might not be incentive compatible if the decisionmaker is ambiguity averse. We propose a slight modification of the procedure in which the randomization takes place before decisions are made and the state is realized, and prove that if subjects evaluate the experimental environment in that way (first  risk, second  uncertainty), incentive compatibility may be restored. 
Keywords:  incentive compatibility, certainty equivalent, probability equivalents, broad bracketing, Ellsberg, BDM, choice list, MPL 
JEL:  C81 C91 D81 
Date:  2021–11–14 
URL:  http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa711&r= 
By:  Marc Fleurbaey (PSE  Paris School of Economics  ENPC  École des Ponts ParisTech  ENS Paris  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  UP1  Université Paris 1 PanthéonSorbonne  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); Stéphane Zuber (PSE  Paris School of Economics  ENPC  École des Ponts ParisTech  ENS Paris  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  UP1  Université Paris 1 PanthéonSorbonne  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:  Utilitarianism plays a central role in economics, but there is a gap between theory, where utilitarianism is dominant, and applications, where monetary criteria are often used. For applications, a key difficulty is to define how utilities should be measured and compared. Drawing on Harsanyi's (1955) approach, we introduce a new normalization of utilities ensuring that: (i) a transfer from a rich population to a poor population is welfare enhancing, and (ii) populations with more riskaverse people have lower welfare. We study some implications of this "fair utilitarianism" for risk sharing, collective risk aversion, and the design of health policy. (JEL D63, D81) 
Date:  2021–05–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03426179&r= 
By:  Yoram Halevy; Emre Ozdenoren 
Abstract:  The Ellsberg experiments provide an intuitive illustration that the Savage approach, which reduces subjective uncertainty to risk, is not rich enough to capture many decision makers' preferences. Experimental evidence suggests that decision makers reduce uncertainty to compound risk. This work presents a theoretical model of decision making in which preferences are defined on both Savage subjective acts and compound objective lotteries. Preferences are twostage probabilistically sophisticated when the ranking of acts corresponds to a ranking of the respective compound lotteries induced by the acts through the decision maker's subjective belief. This family of preferences includes various theoretical models that have been proposed in the literature to accommodate nonneutral attitude towards ambiguity. The principle of calibration, which was used by Ramsey and de Finetti, allows an outside observer to relate preferences over acts and compound objective lotteries. If preferences abide by the calibration axioms, the evaluation of the compound lottery induced by an act through the subjective belief coincides with the valuation of the corresponding compound objective lottery. Calibration provides a foundation to formalize and understand the tight empirical association between probabilistic sophistication and reduction of compound lotteries, for all twostage probabilistically sophisticated preferences. 
Keywords:  ambiguity, probabilistic sophistication, reduction of compound lotteries, Ellsberg 
JEL:  D81 
Date:  2021–11–18 
URL:  http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa713&r= 
By:  Lily, Miriam Al; Liebenehm, Sabine; Waibel, Hermann 
Keywords:  Risk and Uncertainty, Consumer/Household Economics 
Date:  2021–08 
URL:  http://d.repec.org/n?u=RePEc:ags:iaae21:315152&r= 
By:  Costa, Carlos Eugênio da; Maestri, Lucas Jóver; Santos, Marcelo Rodrigues dos 
Abstract:  How should search frictions in the labor market affect distributive policies? Can we assess current realworld policies? After building a framework for answering these questions we show that any constrained efficient allocation must satisfy the following set of testable restrictions: i) earnings and employment probability must be comonotone, ii) wedges on taxable income and employment probability must have the same sign; and; iii) wedges at the bottom of the distribution of income should be positive. Labor income tax schedules and unemployment benefits are shown not to suffice for implementing constrained efficient allocations. Firms can nonetheless be provided incentives to generate the efficient supply of vacancies using informationally feasible tax instruments. We devise a method for the quantitative assessment of inefficiency, calibrate our model to the U.S. economy, and find that it is possible to increase government revenues by 3.48% while preserving everyone’s utility 
Date:  2021–10–15 
URL:  http://d.repec.org/n?u=RePEc:fgv:epgewp:826&r= 
By:  Joseph Kopecky (Department of Economics, Trinity College Dublin); Alan M. Taylor (Department of Economics and Graduate School of Management, University of California, Davis) 
Abstract:  Population aging has been linked to global declines in real interest rates. A similar trend is seen for equity risk premia, which are on the rise. An existing literature can explain part of the declining trend in safe rates using demographics, but has no mechanism to speak to trends in relative returns on different assets. We calibrate a heterogeneous agent lifecycle model with equity markets and aggregate risk, and we show that aging demographics can simultaneously account for both the majority of a downward trend in the risk free rate, while also increasing the return premium attached to risky assets. This is because the lifecycle savings dynamics that have been well documented exert less pressure on risky assets as older households shift away from risk. Under reasonable calibrations we find declines in the safe rate that are considerably larger than most existing estimates between the years 1990 and 2017. We are also able to account for most of the rise in the equity risk premium. Projecting forward to 2050 we show that persistent demographic forces will continue to push the risk free rate further into negative territory, while the equity risk premium remains elevated. 
Keywords:  lifecycle model, demographics, rates of return, safe assets, risky assets, secular stagnation 
JEL:  E21 E43 G11 J11 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:tcd:tcduee:tep1220&r= 
By:  Campi, Luciano; Zabaljauregui, Diego 
Abstract:  Starting from the Avellaneda–Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones under full information, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewisedeterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the market maker needs to adjust for additional regime uncertainty in terms of P&L sensitivity and observed order flow volatility. This effect becomes higher, the longer the waiting time in between orders. 
Keywords:  algorithmic trading; hidden Markov model; highfrequency trading; Market making; piecewisedeterministic Markov processes; stochastic filtering; stochastic optimal control; viscosity solutions 
JEL:  L81 F3 G3 
Date:  2020–05–12 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:104612&r= 
By:  Mikhail Freer; Marco Castillo 
Abstract:  We provide a generalized revealed preference test for quasilinear preferences. The test applies to nonlinear budget sets and nonconvex preferences as those found in taxation and nonlinear pricing contexts. We study the prevalence of quasilinear preferences in a laboratory realeffort task experiment with nonlinear wages. The experiment demonstrates the empirical relevance of our test. We find support for either convex (nonseparable) preferences or quasilinear preferences but weak support for the hypothesis of both quasilinear and convex preferences. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.01248&r= 