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on Utility Models and Prospect Theory |
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Issue of 2023‒04‒17
eighteen papers chosen by |
| By: | Stanca Lorenzo (Department of Economics, Social Studies, Applied Mathematics and Statistics (ESOMAS) and Collegio Carlo Alberto, University of Torino, Italy;) |
| Abstract: | Models of recursive utility are of central importance in many economic applications. This paper investigates a new behavioral feature exhibited by these models: aversion to risks that exhibit persistence (positive autocorrelation) through time, referred to as correlation aversion. I introduce a formal notion of such a property and provide a characterization based on risk attitudes, and show that correlation averse preferences admit a specific variational representation. I discuss how these findings imply that attitudes toward correlation are a crucial behavioral aspect driving the applications of recursive utility in fields such as asset pricing, climate policy, and optimal fiscal policy. |
| Keywords: | Intertemporal Substitution, Risk Aversion, Correlation Aversion, Recursive Utility, Preference for Early Resolution of Uncertainty, Information. |
| JEL: | C61 D81 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:tur:wpapnw:080&r=upt |
| By: | Anastasiya Tanana |
| Abstract: | We consider existence and uniqueness of Nash equilibria in an $N$-player game of utility maximization under relative performance criteria of multiplicative form in complete semimartingale markets. For a large class of players' utility functions, a general characterization of Nash equilibria for a given initial wealth vector is provided in terms of invertibility of a map from $\mathbb{R}^N$ to $\mathbb{R}^N$. As a consequence of the general theorem, we derive existence and uniqueness of Nash equilibria for an arbitrary initial wealth vector, as well as their convergence, if either (i) players' utility functions are close to CRRA, or (ii) players' competition weights are small and relative risk aversions are bounded away from infinity. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.07941&r=upt |
| By: | Nicole B\"auerle; Antje Mahayni |
| Abstract: | We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff et al. (2005)) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a drift distribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. To the best of our knowledge an explicit solution method in this setting is new. We rely on some duality theorems to prove our statements. Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution, i.e. we are able to explain the interaction of risk and ambiguity preferences. We compare our results with the ones in a pre-commitment setup where the investor is restricted to deterministic strategies. It turns out that (under risk and ambiguity aversion) an infinite investment horizon implies in both cases a maximin decision rule, i.e. the investor follows the worst (best) Merton fraction (over all realizations of it) if she is more (less) risk averse than a log-investor. We illustrate our findings with an extensive numerical study. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.08521&r=upt |
| By: | David M\"uller; Emerson Melo; Ruben Schlotter |
| Abstract: | This paper introduces the distributionally robust random utility model (DRO-RUM), which allows the preference shock (unobserved heterogeneity) distribution to be misspecified or unknown. We make three contributions using tools from the literature on robust optimization. First, by exploiting the notion of distributionally robust social surplus function, we show that the DRO-RUM endogenously generates a shock distributionthat incorporates a correlation between the utilities of the different alternatives. Second, we show that the gradient of the distributionally robust social surplus yields the choice probability vector. This result generalizes the celebrated William-Daly-Zachary theorem to environments where the shock distribution is unknown. Third, we show how the DRO-RUM allows us to nonparametrically identify the mean utility vector associated with choice market data. This result extends the demand inversion approach to environments where the shock distribution is unknown or misspecified. We carry out several numerical experiments comparing the performance of the DRO-RUM with the traditional multinomial logit and probit models. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.05888&r=upt |
| By: | Nicole El Karoui (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité); Mohamed Mrad (LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - CNRS - Centre National de la Recherche Scientifique - Université Sorbonne Paris Nord) |
| Abstract: | Decision making under uncertainty is often viewed as an optimization problem under choice criterium, but its calibration raises the "inverse" problem to recover the criterium from the data. An example is the theory of "revealed preference" by Samuelson in the 40s, \cite{samuelson1938}.\\ The observable is a so-called increasing characteristic process $\mbX=(\scX_t(x))$ and the objective is to recover a dynamic stochastic utility $\bfU$ "revealed" in the sense where "$U(t, \scX_t(x))$ is a martingale". A linearized version is provided by the first order conditions $U_x(t, \scX_t(x))=Y_t(u_z(x)$, and the additional martingale conditions of the processes $\scX_x(t, x)Y_t(u_z(x))$ and $\scX_t(x)Y_t(u_z(x))$. When $\mbX$ and $\bfY$ are regular solutions of two SDEs with random coefficients, under strongly martingale condition, any revealed utility is solution of a non linear SPDE, and is the stochastic value function of some optimization problem. More interesting is the dynamic equilibrium problem as in He and Leland \cite{HL}, where $Y$ is coupled with $\scX$ so that the monotonicity of $Y_t(z, u_z(z)) $ is lost. Nevertheless, we solve the He \& Leland problem (in random environment), by characterizing all the equilibria: the adjoint process still linear in $y$ (GBM in Markovian case) and the conjugate utilities are a deterministic mixture of stochastic dual power utilities. Besides, the primal utility is the value function of an optimal wealth allocation in the Pareto problem. |
| Date: | 2021–03–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01966312&r=upt |
| By: | Kislaya Prasad |
| Abstract: | This paper proves a constructive version of the expected utility theorem. The word constructive is construed here in two senses - first, as in constructive mathematics, whereby the logic underlying proofs is intuitionistic. In a second sense of the word, constructive is taken to mean built up from simpler components. Preferences are defined over lotteries that vary continuously over some topological space and are themselves assumed to vary depending upon some underlying process of measurement, deliberation, or observation. The open sets of the topology serve as the possible truth values of assertions about preference and constrain what can be measured, deduced, or observed. Replacing an open set by an open covering of smaller sets serves as a notion of refinement of information, and deductions made for these smaller sets can be combined or collated to yield corresponding deductions over the larger set. The two notions of constructive turn out to be related because the underlying logic of the objects within the system is generally intuitionistic. The classical expected utility theorem is shown to be non-constructive, and a constructive version is proved for the present setting by narrowing the domain of preferences. The representation of preferences is via comparisons of continuous real-valued functions. A version of the classical theorem is obtained by imposing a restriction on the collection of open sets of the topology, which has the effect of making the logic classical. The proof here illustrates a robustness property of constructive results. They can be carried over virtually unchanged to a variety of mathematical settings. Here the set of variable lotteries replaces the sets of lotteries from the classical setting, but there are other possibilities. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.08633&r=upt |
| By: | Hugo E. Ramirez; Rafael Serrano |
| Abstract: | We study investment and insurance demand decisions for an agent in a theoretical continuous-time expected utility maximization model that combines risky assets with an (exogenous) insurable background risk. This risk takes the form of a jump-diffusion process with negative jumps in the return rate of the (self-financed) wealth. The main distinctive feature of our model is that the agent's decision on portfolio choice and insurance demand causes nonlinear friction in the dynamics of the wealth process. We use the dynamic programming approach to find optimality conditions under which the agent assumes the insurable risk entirely, or partially, or purchases total insurance against it. In particular, we consider differential and piece-wise linear portfolio allocation frictions, with differential borrowing and lending rates as our most emblematic example. Finally, we present a mutual-fund separation result and illustrate our results with several numerical examples when the adverse jump risk has Beta distribution. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.04236&r=upt |
| By: | Anna Bogomolnaia (HSE St Petersburg - Higher School of Economics - St Petersburg, University of Glasgow, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Hervé Moulin (University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | When dividing a "manna" Ω of private items (commodities, workloads, land, time slots) between n agents, the individual guarantee is the welfare each agent can secure in the worst case of other agents' preferences and actions. If the manna is nonatomic and utilities are continuous (not necessarily monotone or convex) the minmax utility, that of our agent's best share in the agent's worst partition of the manna, is guaranteed by Kuhn's generalization of divide and choose. The larger maxmin utility—of the agent's worst share in the agent's best partition—cannot be guaranteed even for two agents. If, for all agents, more manna is better than less (or less is better than more), the new bid and choose rules offer guarantees between minmax and maxmin by letting agents bid for the smallest (or largest) size of a share they find acceptable. |
| Keywords: | fair division, divide and choose, guarantees, nonatomic utilities |
| Date: | 2022–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-03886828&r=upt |
| By: | Pierre-Carl Michaud; Pascal St. Amour |
| Abstract: | Annuities, long-term care insurance and reverse mortgages remain unpopular to manage longevity, medical and housing price risks after retirement. We analyze low demand using a life-cycle model structurally estimated with a unique stated-preference survey experiment of Canadian households. Low risk aversion, substitution between housing and consumption and low marginal utility when in poor health explain most of the reduced demand. Bequests motives are found to be a luxury good and play a limited role. The remaining disinterest is explained by information frictions and behavioural status-quo biases. We find evidence of strong spousal co-insurance motives motivating LTCI and of responsiveness to bundling with a near doubling of demand for annuities when reverse mortgages can be used to annuitize, instead of consuming home equity. |
| JEL: | G51 G53 I13 J14 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31038&r=upt |
| By: | Katsutoshi WAKAI |
| Abstract: | This paper is a multi-period extension of the factor pricing model under ambiguity as developed by Wakai (2018). |
| Keywords: | Ambiguity aversion, asset pricing, factor pricing |
| JEL: | D81 G11 G12 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:kue:epaper:e-22-012&r=upt |
| By: | David Ronayne (European School of Management and Technology (ESMT Berlin)); Roberto Veneziani (Queen Mary University of London); William R. Zame (University of California at Los Angeles) |
| Abstract: | Abstract: Anscombe and Aumann (1963) offer a definition of subjective probability in terms of comparisons with objective probabilities. That definition – which has provided the basis for much of the succeeding work on subjective probability – presumes that the subjective probability of an event is independent of the prize consequences of that event, a property we term Prize Independence. We design experiments to test Prize Independence and find that a large fraction of our subjects violate it; thus, they do not have subjective probabilities. These findings raise questions about the empirical relevance of much of the literature on subjective probability. |
| Keywords: | subjective probability, choice under uncertainty, online experiments. |
| JEL: | D01 D81 D84 |
| Date: | 2022–06–22 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:940&r=upt |
| By: | Sandro Ambuehl; Sebastian Blesse; Philipp Doerrenberg; Christoph Feldhaus; Axel Ockenfels |
| Abstract: | Much economic analysis derives policy recommendations based on social welfare criteria intended to model the preferences of a policy maker. Yet, little is known about policy maker's normative views in a way amenable to this use. In a behavioral experiment, we elicit German legislators' social welfare criteria unconfounded by political economy constraints. When resolving preference conflicts across individuals, politicians place substantially more importance on least-favored than on most-favored alternatives, contrasting with both common aggregation mechanisms and the equal weighting inherent in utilitarianism and the Kaldor-Hicks criterion. When resolving preference conflicts within individuals, we find no support for the commonly used "long-run criterion" which insists that choices merit intervention only if the lure of immediacy may bias intertemporal choice. Politicians' and the public's social welfare criteria largely coincide. |
| Keywords: | Positive welfare economics, politicians, preference aggregation, paternalism |
| JEL: | C90 D60 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ifowps:_391&r=upt |
| By: | Jean-Pierre Drugeon (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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 Panthéon-Sorbonne - ENS-PSL - 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); Thai Ha-Huy (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay) |
| Abstract: | This article introduces an axiomatic approach of utilities streams based upon three preference relations, namely the close future order, the distant future order, and the main order. Assuming all these preferences to be bi-separable, the article derives a unanimous representation for weights over periods. The analysis of two categories of a \emph{potentially better} property allows for the establishment of \textit{MaxMin}, \textit{MaxMax}, and $\alpha-$\textit{MaxMin} representations. This is followed by the presentation of a multiple discounts rates version of $T^{*}$-temporally biased, generalizing quasi-hyperbolic discounting for the close future order. A similar analysis for the distant future is also performed, where it is proved that Banach limits can be considered as the distant future counterpart of exponential discounting in the evaluation of the close future. |
| Keywords: | Axiomatisation, Multiple Discounts, α−MaxMin Citeria, Temporal Biases, Banach Limits |
| Date: | 2023–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:hal-04010969&r=upt |
| By: | Zhengyang Jiang; Cameron Peng; Hongjun Yan |
| Abstract: | We survey thousands of affluent American investors to examine the relationship between personalities and investment decisions. The Big Five personality traits correlate with investors' beliefs about the stock market and economy, risk preferences, and social interaction tendencies. Two personality traits, Neuroticism and Openness, stand out in their explanatory power for equity investments. Investors with high Neuroticism and those with low Openness tend to allocate less investment to equities. We examine the underlying mechanisms and find evidence for both standard channels of preferences and beliefs and other nonstandard channels. We show consistent out-of-sample evidence in representative panels of Australian and German households. |
| JEL: | D91 G11 G41 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31041&r=upt |
| By: | John Quiggin (School of Economics, University of Queensland, Brisbane, Australia) |
| Abstract: | Reducing ambiguity to a purely technical property of preferences misses much of the insight in Ellsberg’s (1961) paper, as well as in more recent developments in the study of differential awareness. In this paper, syntac- tic approaches to ambiguity are used to illustrate the point that Reducing ambiguity to a purely technical property of preferences misses much of the insight in Ellsberg’s (1961) paper, as well as in more recent developments in the study of differential awareness. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:662&r=upt |
| By: | Benjamin Enke; Thomas Graeber; Ryan Oprea |
| Abstract: | We provide experimental evidence that core intertemporal choice anomalies -- including extreme short-run impatience, structural estimates of present bias, hyperbolicity and transitivity violations -- are driven by complexity rather than time or risk preferences. First, all anomalies also arise in structurally similar atemporal decision problems involving valuation of iteratively discounted (but immediately paid) rewards. These computational errors are strongly predictive of intertemporal decisions. Second, intertemporal choice anomalies are highly correlated with indices of complexity responses including cognitive uncertainty and choice inconsistency. We show that model misspecification resulting from ignoring behavioral responses to complexity severely inflates structural estimates of present bias. |
| JEL: | D03 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31047&r=upt |
| By: | Yuechen Dai; Richard Watt (University of Canterbury) |
| Abstract: | The problem of insurer insolvency has almost exclusively been seen as an issue in regulation. However, it is also clear that there is an obvious element of asymmetric information present when insolvency is possible. Insurers are clearly better informed of their probability of defaulting on an insurance arrangement than are their insureds, and just as clearly, that probability affects the value of the contract to the insured. With that in mind, we recast the issue of insurer insolvency within the context of asymmetric information, specifically, adverse selection. In our model, the (risk-neutral) insurer is the informed agent, and the (risk-averse) policyholder is the uninformed principal. Thereby, the classic player identities in an asymmetric information problem are reversed. We find equilibrium contract menus for the cases of perfect competition between insurers, and for the case of a single monopolistic insurer. |
| Keywords: | Insurance insolvency, asymmetric information, adverse selection |
| JEL: | D80 D82 |
| Date: | 2023–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:23/02&r=upt |
| By: | St\'ephane Gonzalez; Nikolaos Pnevmatikos |
| Abstract: | The axiomatic foundations of Bentham and Rawls solutions are discussed within the broader domain of cardinal preferences. It is unveiled that both solution concepts share all four of the following axioms: Nonemptiness, Anonymity, Unanimity, and Continuity. In order to fully characterize the Bentham and Rawls solutions, three variations of a consistency criterion are introduced and their compatibility with the other axioms is assessed. Each expression of consistency can be interpreted as a property of decision-making in uncertain environments. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.07488&r=upt |