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on Utility Models and Prospect Theory |
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Issue of 2024‒01‒15
thirteen papers chosen by |
| By: | Roger J. A. Laeven; Mitja Stadje |
| Abstract: | This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space $\Delta$ of probabilities, a probability weighting function $\psi$, generating the measure $\nu_{\psi}$ by transforming an objective probability measure, and a utility function $\phi$, such that, for all $\tilde{v}, \tilde{u}\in\tilde{V}$, \begin{align*} \tilde{v}\succeq\tilde{u} \Leftrightarrow \min_{Q \in \Delta} \left\{\mathbb{E}_Q\left[\int\phi\left(\tilde{v}^{\centerdot}\right)\, \mathrm{d}\nu_{\psi}\right]+c(Q)\right\} \geq \min_{Q \in \Delta} \left\{\mathbb{E}_Q\left[\int\phi\left(\tilde{u}^{\centerdot}\right)\, \mathrm{d}\nu_{\psi}\right]+c(Q)\right\}. \end{align*} Our theory extends the rank-dependent utility model of Quiggin (1982) for decision under risk to risk and ambiguity, reduces to the variational preferences model when $\psi$ is the identity, and is dual to variational preferences when $\phi$ is affine in the same way as the theory of Yaari (1987) is dual to expected utility. As a special case, we obtain a preference axiomatization of a decision theory that is a rank-dependent generalization of the popular maxmin expected utility theory. We characterize ambiguity aversion in our theory. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.05977&r=upt |
| By: | Antonio Villar (Department of Economics, Universidad Pablo de Olavide) |
| Abstract: | We propose in this paper a poverty index that considers poverty persistence as an integral part of poverty measurement. Poverty is regarded as a social welfare loss in a multiperiod scenario. Using familiar tools (logarithmic utilities and a utilitarian social welfare function) we obtain a poverty index which is mathematically simple, easy to interpret, that can be decomposed into incidence, intensity, and inequality, and is additively decomposable by population subgroups. It consists of the log of the geometric mean of individual intertemporal utility losses. |
| Keywords: | Poverty persistence, welfares loss, logarithmic utility, utilitarian, decomposability. |
| JEL: | D31 I32 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:pab:wpaper:23.11&r=upt |
| By: | Weixuan Xia |
| Abstract: | The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as patience, socialization effects, and market volatility. The market is composed of multiple risky assets and multiple consumption goods, while in addition there are multiple fluctuating preference parameters with inexact values connected to imprecise tastes. Utility maximization is a multi-criteria problem with possibly function-valued criteria. To come up with a complete characterization of the solutions, first we motivate and introduce a set-valued stochastic process for the dynamics of multi-utility indices and formulate the optimization problem in a topological vector space. Then, we modify a classical scalarization method allowing for infiniteness and randomness in dimensions and prove results of equivalence to the original problem. Illustrative examples are given to demonstrate practical interests and method applicability progressively. The link between the original problem and a dual problem is also discussed, relatively briefly. Finally, using Malliavin calculus with stochastic geometry, we find optimal investment policies to be generally set-valued, each of whose selectors admits a four-way decomposition involving an additional indecisiveness risk-hedging portfolio. Our results touch on new directions for optimal consumption--investment choices in the presence of incomparability and time inconsistency, also signaling potentially testable assumptions on the variability of asset prices. Simulation techniques for set-valued processes are studied for how solved optimal policies can be computed in practice. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00266&r=upt |
| By: | SHINOZAKI, Hiroki |
| Abstract: | We study a problem of assigning packages of objects to agents with money. We allow agents to have utility functions that exhibit income effects or face hard budget constraints. It is already known that one of income effects and hard budget constraints lead to the non-existence of a rule satisfying strategy-proofness, efficiency, individual rationality, and no subsidy (Dobzinski et al., 2012; Kazumura and Serizawa, 2016; Baisa; 2020, Malik and Mishra, 2021, etc.). Given such negative results, we search for rules satisfying non-obvious manipulability (Troyan and Morrill, 2020), an incentive property weaker than strategy-proofness, together with the other three properties. First, we identify a necessary and sufficient condition for a rule satisfying efficiency, individual rationality, and no subsidy to be non-obviously manipulable. By using the first result, we show that a slight modification of a (truncated) pay as bid rule satisfies non-obvious manipulability, efficiency, individual rationality, and no subsidy. |
| Keywords: | Non-obvious manipulations, Efficiency, Strategy-proofness, Non-quasi-linear utilities, Hard budget constraints, Package auctions |
| JEL: | D44 D47 D71 D82 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hiasdp:hias-e-136&r=upt |
| By: | Weiye Yang |
| Abstract: | A backward stochastic differential equation (BSDE) is an SDE of the form $-dY_t = f(t, Y_t, Z_t)dt - Z_t^*dW_t;\ Y_T = \xi$. The subject of BSDEs has seen extensive attention since their introduction in the linear case by Bismut (1973) and in the general case by Pardoux and Peng (1990). In contrast with deterministic differential equations, it is not enough to simply reverse the direction of time and treat the terminal condition as an initial condition, as we would then run into problems with adaptedness. Intuitively, our "knowledge" at time $t$ consists only of what has happened at all times $s \in [0, t]$, and we cannot reverse the direction of time whilst keeping this true. The layout of this essay is as follows: In Section 1 we introduce BSDEs and go over the basic results of BSDE theory, including two major theorems: the existence and uniqueness of solutions and the comparison theorem. We also introduce linear BSDEs and the notion of supersolutions of a BSDE. In Section 2 we set up the financial framework in which we will price European contingent claims, and prove a result about the fair price of such claims in a dynamically complete market. In Section 3 we extend the theory of linear BSDEs to include concave BSDEs, and apply this to pricing claims in more complicated market models. In Section 4 we take a look at utility maximisation problems, and see how utilising BSDE theory allows for a relatively simple and neat solution in certain cases. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.06690&r=upt |
| By: | Bogliacino, Francesco (Universidad Nacional de Colombia); Aycinena, Diego (Universidad del Rosario); Kimbrough, Erik |
| Abstract: | We analyze and compare three methods of measuring norms: the Krupka and Weber (KW) coordination game, the two-step approach by Bicchieri and Xiao (BX), and a novel Binarized Scoring Method (BSM) we introduce that elicits the full distribution of normative beliefs. We test their effectiveness in two distinctive ways. First, we compare the fit and predictive power of the norms elicited by each method in 3 versions of the dictator game, which differ in how the pie is initially allocated. Then we use vignettes to assess the extent to which the methods can recover existing norms for various naturally occurring settings. We find that the KW method yields better predictive power within a norm-dependent utility model. All 3 methods effectively recover norms in field settings, although KW is more robust to false positives. |
| Date: | 2023–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:djfw5&r=upt |
| By: | Miaomiao Dong; Tatiana Mayskaya; Vladimir Smirnov; Olivia Taylor; Andrew Wait |
| Abstract: | From corporate boards to innovative teams, the benefits of diversity are increasingly being praised. In this paper, we investigate how optimal cognitive diversity depends on the nature of production and the objective criterion employed. With a utilitarian objective, when the output of the most productive worker becomes relatively more important, optimal diversity weakly increases. To capture the preferences of a public service provider, a regulated firmor a very risk averse manager, we also consider a Rawlsian objective. While optimal diversity under the Rawlsian objective might decrease as the output of the most productive worker becomes relatively more important, optimal diversity is alwaysweakly higherwith the Rawlsian objective than with the utilitarian one. Our result suggests that a diverse outcome can be achieved by adjusting a team’s objective rather than controlling diversity directly. |
| Keywords: | cognitive diversity, submodular, supermodular, teams, utilitarian, Rawlsian objective |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2023-10&r=upt |
| By: | Francesco Fallucchi (Department of Economics, University of Bergamo); Francesco Trevisan (Department of Economics, Ca' Foscari University of Venice) |
| Abstract: | We study the Tullock contest model with desert concerns (Gill and Stone (2010)). In a contest with n possibly heterogeneous players and convex effort costs, we establish the conditions necessary for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of desert concerns on players' spending behavior, probability of winning, and rent dissipation. |
| Keywords: | rent-seeking, contest, asymmetry, desire to win, loss aversion |
| JEL: | D31 D72 D91 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2023:31&r=upt |
| By: | Linden, Mikael; Väänänen, Niko |
| Abstract: | We propose an elementary economic model which assumes that the integral of life survival function can be interpreted as a utility function. The model helps us to understand connections between individual’s survival estimate to some specific age and the timing of retirement. The difference between survival and related longevity costs is maximized with an estimate of survival time. The results are derived with the concept of restricted mean survival times (RMST). This is also applied to the observed retirement and death ages for the Finnish year 1947 birth cohort. We show that actual survival times, i.e., mean lifetimes to the age of 73 years, which is the highest age in our follow-up sample, differ among retired and not yet retired persons between the ages from 60 to 68 years. The main result is that persons who retire in ages from 62 to 66 years have shorter mean lifetimes to the age of 73 years compared to individuals who do not retire in these ages. This is interpreted as evidence of too optimistic survival estimates among the persons retiring at the most popular retirement ages. |
| Keywords: | Retirement ages, subjective survival times, age of death, survival analysis, restricted mean survival times (RMST |
| JEL: | C41 I12 J14 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:119344&r=upt |
| By: | Tim J. Boonen; Xia Han |
| Abstract: | This paper studies an optimal insurance contracting problem in which the preferences of the decision maker given by the sum of the expected loss and a convex, increasing function of a deviation measure. As for the deviation measure, our focus is on convex signed Choquet integrals (such as the Gini coefficient and a convex distortion risk measure minus the expected value) and on the standard deviation. We find that if the expected value premium principle is used, then stop-loss indemnities are optimal, and we provide a precise characterization of the corresponding deductible. Moreover, if the premium principle is based on Value-at-Risk or Expected Shortfall, then a particular layer-type indemnity is optimal, in which there is coverage for small losses up to a limit, and additionally for losses beyond another deductible. The structure of these optimal indemnities remains unchanged if there is a limit on the insurance premium budget. If the unconstrained solution is not feasible, then the deductible is increased to make the budget constraint binding. We provide several examples of these results based on the Gini coefficient and the standard deviation. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.01813&r=upt |
| By: | Maarten Meeuwis; Dimitris Papanikolaou; Jonathan L. Rothbaum; Lawrence D.W. Schmidt |
| Abstract: | We show that time variation in risk premia leads to time-varying idiosyncratic income risk for workers. Using US administrative data on worker earnings, we show that increases in risk premia lead to lower earnings for low-wage workers; these declines are primarily driven by job separations. By contrast, productivity shocks affect the earnings mainly of highly paid workers. We build an equilibrium model of labor market search that quantitatively replicates these facts. The model generates endogenous time-varying income risk in response to changes in risk premia and matches several stylized features of the data regarding unemployment and income risk over the business cycle. |
| JEL: | E3 E40 G1 J20 J30 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31968&r=upt |
| By: | Sophie Zhou; Frederick van der Ploeg; Rick van der Ploeg |
| Abstract: | We study climate change in a model with a carbon-intensive and a green sector, each subject to stochastic sectoral productivity shocks, and show how the underlying economic structure affects the risk-adjusted discount rate and the climate risk premium in the social cost of carbon (SCC). Consumption growth, aggregate consumption volatility, and the climate beta are all affected by the elasticity of substitution between the two sectors and the relative size of the sectors, and vary as the green transition progresses. The climate risk premium is hump-shaped during the green transition, with the climate beta playing a dominant role in its magnitude. For sufficiently strong substitutability between the two sectors and sufficiently low correlation between the sectoral shocks, decarbonisation can temporarily reduce aggregate consumption risk, as the climate beta becomes negative in the mid phase of the transition. The risk-adjusted discount rate first falls then rises during the green transition, leading to a SCC to GDP ratio that rises then falls as the green sector grows. We illustrate our analytical results numerically. |
| Keywords: | social cost of carbon, climate beta, carbon risk premium, two-sector model, asset pricing |
| JEL: | E60 G12 H23 O41 Q54 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10840&r=upt |
| By: | Andrey Duván Rincón-Torres; Andrés Felipe Salas-Avila; Juan Manuel Julio-Román |
| Abstract: | We study the behaviour of three quantitative sample surveys and a non sample inflation expectation report for Colombia. We found that expectations in Colombia; (i) are not strongly, i.e. a la Muth, rational because they show cross-section disagreement, (ii) expectations, however, show some features of weak rationality, (iii) expectations disagreement is time varying and relate to inflation, inflation changes and the output gap, thus suggesting a staggered information flow to agents, (iv) the forecast error loss function employed by agents is not symmetric and increasingly penalizes higher expectations than finally observed inflation as the horizon grows, and (v) this fact also explains the stylised fact that observed expectation share with theoretical rational expectations that expectations look like lagged versions of inflation that dampen with the horizon. The latest finding also arises from a very general econometric set up we develop in this paper. These results imply that the effect of weakening the rational expectations assumption in Colombian monetary policy models should be assessed, especially when compared to sticky information and heterogeneous agents choosing non Mean Square forecast Error losses. **** RESUMEN: Analizamos tres encuestas cuantitativas muestrales y un reporte no muestral de expectativas de inflación para Colombia. Encontramos que las expectativas en Colombia:(i) no son fuertemente, a la Muth, racionales debido a que exhiben descuerdo en cada corte transversal; (ii) sin embargo, muestran características de racionalidad débil; (iii) el desacuerdo es tiempo variante y se relaciona con la inflación, sus cambios y la brecha del PIB, sugiriendo un flujo escalonado de la información para formularlas; (iv) la función de pérdida ante errores de expectativas no es simétrica y penaliza de forma creciente las expectativas más altas que la inflación observada en la medida que se extiende el horizonte; y (v) este resultado explica también el hecho estilizado que comparten las expectativas observadas y las teóricas que las expectativas parecen versiones rezagadas de la inflación observada que se suavizan con el horizonte. Este hallazgo surge también de un esquema econométrico muy general que desarrollamos en este artículo. Estos resultados implican que se debe establecer el efecto de debilitar el supuesto de expectativas racionales en los modelos para la política monetaria, especialmente cuando se comparan con modelos con flujos escalonados de información y agentes heterogéneos que escogen funciones de pérdida distintas al Error Cuadrático Medio de pronósticos. |
| Keywords: | Inflation Expectations, expectation disagreement, near unit root, weak and strong rationality, non symmetric loss function, Expectativas de inflación, desacuerdo de las expectativas, cercanía a una raíz unitaria, Racionalidad débil y fuerte, función de pérdida asimétrica |
| JEL: | C53 C82 E31 E37 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:bdr:borrec:1262&r=upt |