nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2020‒06‒15
nineteen papers chosen by
Alexander Harin
Modern University for the Humanities

  1. Forward BSDEs and backward SPDEs for utility maximization under endogenous pricing By Thai Nguyen; Mitja Stadje
  2. Ambiguous Business Cycles: A Quantitative Assessment By Altug, Sumru; Collard, Fabrice; Cakmakli, Cem; Mukerji, Sujoy; Ozsöylev, Han
  3. Introduction to sub-interval analysis. Estimations for the centers of gravity By Harin, Alexander
  4. Non-concave expected utility optimization with uncertain time horizon: an application to participating life insurance contracts By Christian Dehm; Thai Nguyen; Mitja Stadje
  5. Forward utilities and Mean-field games under relative performance concerns By Goncalo dos Reis; Vadim Platonov
  6. Functional Decision Theory in an Evolutionary Environment By Noah Topper
  7. Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time By Ying Hu; Hanqing Jin; Xun Yu Zhou
  8. Analysis of Health Care Utilization in Côte d'Ivoire By Alimatou Cisse
  9. Asset pricing with endogenous state-dependent risk aversion By Rachida Ouysse
  10. Inequality Aversion, Externalities, and Pareto-Efficient Income Taxation By Aronsson, Thomas; Johansson-Stenman, Olof
  11. Semiparametric Estimation of Dynamic Binary Choice Panel Data Models By Fu Ouyang; Thomas Tao Yang
  12. Funding Public Projects: A Case for the Nash Product Rule By Florian Brandl; Felix Brandt; Dominik Peters; Christian Stricker; Warut Suksompong
  13. Revealing gender-specific costs of STEM in an extended Roy model of major choice By Marc Henry; Romuald Meango; Ismael Mourifie
  14. Predictive Power in Behavioral Welfare Economics By Elias Bouacida; Daniel Martin
  15. Information weighting under least squares learning By Jaqueson K. Galimberti
  16. Effects of Changes in Exchange Rate Volatility on Short-run Equilibrium in International Oligopoly By Tetsuya Shinkai; Takao Ohkawa; Makoto Okamura; Ryoma Kitamura
  17. Statistical inference for the EU portfolio in high dimensions By Taras Bodnar; Solomiia Dmytriv; Yarema Okhrin; Nestor Parolya; Wolfgang Schmid
  18. On Investment and Cycles in Explicitely Solved Vintage Capital Models By Hippolyte d'Albis; Jean-Pierre Drugeon
  19. A Comparison of Living Standards Across the States of America By Elena Falcettoni; Vegard Nygaard

  1. By: Thai Nguyen; Mitja Stadje
    Abstract: We study the expected utility maximization problem of a large investor who is allowed to make transactions on a tradable asset in a financial market with endogenous permanent market impacts as suggested in [24] building on [6, 7]. The asset price is assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. We show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) which is equivalent to a highly non-linear backward stochastic partial differential equation (BSPDE). Existence results can be achieved in the case where the driver function of the representative market maker is quadratic or the utility function of the large investor is exponential. Explicit examples are provided when the market is complete or the driver function is positively homogeneous.
    Date: 2020–05
  2. By: Altug, Sumru; Collard, Fabrice; Cakmakli, Cem; Mukerji, Sujoy; Ozsöylev, Han
    Abstract: In this paper, we examine the cyclical dynamics of a Real Business Cycle model with ambiguity averse consumers and investment irreversibility using the smooth ambiguity model of Klibanoff et al. (2005, 2009). Ambiguity of belief about the productivity process arises as agents do not know the process driving variation in aggregate TFP, and they must make inferences regarding the true process at the same time as they infer the behavior of the unobserved temporary component using a Kalman filtering algorithm. Our findings may be summarized as follows. First, the standard business cycle facts hold in our framework, which are not altered significantly by changes in the degree of ambiguity aversion. Second, we demonstrate a role for information and learning effects, and show that lower initial ambiguity or greater confidence coupled with learning dynamics lowers the volatility and increases the persistence in all of the key macroeconomic variables. Third, comparing the performance of our model to the New Keynesian business cycle model of Ilut and Schneider (2014) with maxmin expected utility, we find that the version of their model without nominal and real frictions turns out to have limited success at matching the moments for the quantity variables. In the maxmin expected utility framework, the worst case scenario instills too much caution on the part of agents who, in the absence of a key set of nominal and real frictions, end up excessively reducing their responses to TFP shocks.
    JEL: C6 D8 E2
    Date: 2020–05
  3. By: Harin, Alexander
    Abstract: An introduction to a sub-interval analysis (SI analysis or SIA) namely to a SI arithmetic is presented. Prerequisites and possible applications of the SIA are reviewed. A system of definitions of the SIA is formulated. New basic formulae are obtained. Some examples are considered including estimations of the minimal values of forbidden zones for measurements in behavioral economics. The article is concentrated mainly on estimations for the centers of gravity.
    Keywords: expectation; moments; mathematic; utility theory; prospect theory; behavioral economics; psychology; social sciences;
    JEL: C02 C1 D8
    Date: 2020–05–18
  4. By: Christian Dehm; Thai Nguyen; Mitja Stadje
    Abstract: We examine an expected utility maximization problem with an uncertain time horizon, a classical example being a life insurance contract due at the time of death. Life insurance contracts usually have an option-like form leading to a non-concave optimization problem. We consider general utility functions and give necessary and sufficient optimality conditions, deriving a computationally tractable algorithm. A numerical study is done to illustrate our findings. Our analysis suggests that the possible occurrence of a premature stopping leads to a reduced performance of the optimal portfolio compared to a setting without time-horizon uncertainty.
    Date: 2020–05
  5. By: Goncalo dos Reis; Vadim Platonov
    Abstract: We introduce the concept of mean field games for agents using Forward utilities to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.
    Date: 2020–05
  6. By: Noah Topper
    Abstract: Functional decision theory (FDT) is a fairly new mode of decision theory and a normative viewpoint on how an agent should maximize expected utility. The current standard in decision theory and computer science is causal decision theory (CDT), largely seen as superior to the main alternative evidential decision theory (EDT). These theories prescribe three distinct methods for maximizing utility. We explore how FDT differs from CDT and EDT, and what implications it has on the behavior of FDT agents and humans. It has been shown in previous research how FDT can outperform CDT and EDT. We additionally show FDT performing well on more classical game theory problems and argue for its extension to human problems to show that its potential for superiority is robust. We also make FDT more concrete by displaying it in an evolutionary environment, competing directly against other theories.
    Date: 2020–05
  7. By: Ying Hu (IRMAR - Institut de Recherche Mathématique de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique - ENS Rennes - École normale supérieure - Rennes - UR2 - Université de Rennes 2 - UNIV-RENNES - Université de Rennes - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - AGROCAMPUS OUEST); Hanqing Jin (University of Oxford [Oxford]); Xun Yu Zhou
    Abstract: We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of sophisticated consistent planners who seek (subgame perfect) intra-personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than 1 corresponding to an effective reduction in risk premium due to probability weighting.
    Keywords: Rank-dependent utility,probability weighting,portfolio selection,con- tinuous time,time inconsistency,intra-personal equilibrium strategy,market price of risk
    Date: 2020–05–26
  8. By: Alimatou Cisse (Department of Economy and Management University of Cocody Abidjan, Côte d'Ivoire)
    Abstract: Health constitutes a sufficiently solid entrance to reduce poverty and promote economic growth. Yet, in most African countries and particularly in Côte d’Ivoire, the populations’ state of health has seen a real deterioration over the last decade. This study seeks to explain this decline by determining the explanatory factors of recourse to health care providers. To this end, the multinomial logit model is used. The theoretical basis for this analysis is the maximization of a utility function to produce health. The data to test the study’s hypotheses came from the survey of the National Institute of Statistics, entitled Social Dimension of Structural Adjustment, carried out in April 1993. The results show that the education level of the household head, the household’s income, the price of medication, and the time to reach the health care provider (as a proxy for the distance to a health care provider) determine the choice for a specific health care provider. The level of education and the income positively influence this choice, while the cost of medication and the time to provider (time to reach the health provider) negatively influence the choice of health care provider.
  9. By: Rachida Ouysse (School of Economics, UNSW Business School, UNSW)
    Abstract: We present an economy where aggregate risk aversion is stochastic and state-dependent in response to information about the wider economy. A factor model is used to link aggregate risk aversion to the business cycle and to handle high-dimensionality of the information about the economy. Our estimated aggregate risk aversion is counter-cyclical and varies with news about economic booms and busts. We find new evidence of volatility clustering of risk aversion around recessions. In addition to the price of consumption risk associated with consumption risk, time variation in risk aversion introduces risk preferences as a new component of the risk premium.
    Keywords: Consumption-based capital asset pricing model; time-varying risk aversion; GMM estimation; Euler equations; mispricing; Counter-cyclicality.
    Date: 2020–01
  10. By: Aronsson, Thomas (Department of Economics, Umeå University); Johansson-Stenman, Olof
    Abstract: This paper analyzes Pareto-efficient marginal income taxation taking into account externalities induced through individual inequality aversion, meaning that people have preferences for equality. In doing so, we distinguish between four different and widely used models of inequality aversion. The results show that empirically and experimentally quantified degrees of inequality aversion have potentially very strong implications for Pareto-efficient marginal income taxation. It also turns out that the type of inequality aversion (self-centered vs. non-self-centered), and the specific measures of inequality used, matter a great deal. For example, based on simulation results mimicking the disposable income distribution in the U.S., the preferences suggested by Fehr and Schmidt (1999) imply monotonically increasing marginal income taxes, with large negative marginal tax rates for low-income individuals and large positive marginal tax rates for high-income ones. In contrast, the in many respects comparable model by Bolton and Ockenfels (2000) implies close to zero marginal income tax rates for all.
    Keywords: Pareto-efficient taxation; Inequality aversion; Self-centered inequality aversion; Non-self-centered inequality aversion; Fehr and Schmidt preferences; Bolton and Ockenfels preferences; GINI coefficient; Coefficient of variation
    JEL: D03 D62 H23
    Date: 2020–05–18
  11. By: Fu Ouyang; Thomas Tao Yang
    Abstract: We propose a new approach to the semiparametric analysis of panel data binary choice models with fixed effects and dynamics (lagged dependent variables). The model we consider has the same random utility framework as in Honore and Kyriazidou ´ (2000). We demonstrate that, with additional serial dependence conditions on the process of deterministic utility and tail restrictions on the error distribution, the (point) identification of the model can proceed in two steps, and only requires matching the value of an index function of explanatory variables over time, as opposed to that of each explanatory variable. Our identification approach motivates an easily implementable, two-step maximum score (2SMS) procedure – producing estimators whose rates of convergence, in contrast to Honore and Kyriazidou ´ ’s (2000) methods, are independent of the model dimension. We then derive the asymptotic properties of the 2SMS procedure and propose bootstrap-based distributional approximations for inference. Monte Carlo evidence indicates that our procedure performs adequately in finite samples. We then apply the proposed estimators to study labor market dependence and the effects of health shocks, using data from the Household, Income and Labor Dynamics in Australia (HILDA) survey.
    Keywords: Semiparametric estimation; Binary choice model; Panel data; Fixed effects; Dynamics; Maximum score; Bootstrap
    JEL: C14 C23 C35
    Date: 2020–05
  12. By: Florian Brandl; Felix Brandt; Dominik Peters; Christian Stricker; Warut Suksompong
    Abstract: We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for participatory budgeting without an exogenously available budget, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents report linear utility functions over projects together with the amount of their contributions, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism---the Nash product rule---which picks the distribution that maximizes the product of the agents' utilities. This rule is Pareto efficient, and we prove that it satisfies attractive incentive properties: the Nash rule spends an agent's contribution only on projects the agent finds acceptable, and it provides strong participation incentives. We also discuss issues of strategyproofness and monotonicity.
    Date: 2020–05
  13. By: Marc Henry; Romuald Meango; Ismael Mourifie
    Abstract: We derive sharp bounds on the non consumption utility component in an extended Roy model of sector selection. We interpret this non consumption utility component as a compensating wage differential. The bounds are derived under the assumption that potential wages in each sector are (jointly) stochastically monotone with respect to an observed selection shifter. The lower bound can also be interpreted as the minimum cost subsidy necessary to change sector choices and make them observationally indistinguishable from choices made under the classical Roy model of sorting on potential wages only. The research is motivated by the analysis of women's choice of university major and their underrepresentation in mathematics intensive fields. With data from a German graduate survey, and using the proportion of women on the STEM faculty at the time of major choice as our selection shifter, we find high costs of choosing the STEM sector for women from the former West Germany, especially for low realized incomes and low proportion of women on the STEM faculty, interpreted as a scarce presence of role models.
    Date: 2020–05
  14. By: Elias Bouacida; Daniel Martin
    Abstract: When choices are inconsistent due to behavioral biases, there is a theoretical debate about whether the structure of a model is necessary for providing precise welfare guidance based on those choices. To address this question empirically, we use standard data sets from the lab and field to evaluate the predictive power of two “model-free†approaches to behavioral welfare analysis. We find they typically have high predictive power, which means there is little ambiguity about what should be selected from each choice set. We also identify properties of revealed preferences that help to explain the predictive power of these approaches.
    Keywords: Welfare economics, behavioral economics, predictive power, revealed preferences
    JEL: I30 C91 D12
    Date: 2020
  15. By: Jaqueson K. Galimberti
    Abstract: This paper evaluates how adaptive learning agents weight different pieces of information when forming expectations with a recursive least squares algorithm. The analysis is based on a renewed and more general non-recursive representation of the learning algorithm, namely, a penalized weighted least squares estimator, where a penalty term accounts for the effects of the learning initials. The paper then draws behavioral implications of alternative specifications of the learning mechanism, such as the cases with decreasing, constant, regime-switching, adaptive, and age-dependent gains, as well as practical recommendations on their computation. One key new finding is that without a proper account for the uncertainty about the learning initial, a constant-gain can generate a time-varying profile of weights given to past observations, particularly distorting the estimation and behavioral interpretation of this mechanism in small samples of data. In fact, simulations and empirical estimation of a Phillips curve model with learning indicate that this particular misspecification of the initials can lead to estimates where inflation rates are less responsive to expectations and output gaps than in reality, or “flatter” Phillips curves.
    Keywords: bounded rationality, expectations, adaptive learning, memory
    JEL: D83 D84 D90 E37 C32 C63
    Date: 2020–05
  16. By: Tetsuya Shinkai (School of Economics, Kwansei Gakuin University); Takao Ohkawa (Faculty of Economics,Ritsumeikan University); Makoto Okamura (Faculty of Economics,Gakushuin University); Ryoma Kitamura (Faculty of Economics,Otemon Gakuin University)
    Abstract: This paper investigates exchange rate volatility in an international oligopolistic market in a foreign country that accepts affiliate firms through foreign direct investment. The affiliate firms must procure intermediate products from their overseas parent firms. We derive a Cournot equilibrium of a market in which affiliate firms compete with local firms under foreign exchange rate uncertainty. In equilibrium, we show that affiliates aggressively expand output and the ex-post expected profits and ex-ante certainty equivalence of the affiliates’ profits increase / decrease with a rise in exchange rate risk when the relative risk aversion coefficient is small / large.
    Keywords: risk aversion, exchange rate volatility, short-run equilibria, and international oligopoly
    JEL: G32 L13 L12
    Date: 2020–05
  17. By: Taras Bodnar; Solomiia Dmytriv; Yarema Okhrin; Nestor Parolya; Wolfgang Schmid
    Abstract: In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $c\in(0,1)$ as $n\to\infty$. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S\&P 500 constituents.
    Date: 2020–05
  18. By: Hippolyte d'Albis (PSE - Paris School of Economics); Jean-Pierre Drugeon (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - 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: The purpose of this contribution is to consider a discrete time formulation that would allow for clarifying some salient features of a vintage based understanding of the capital stock..ree main lines of conclusions are established on an analytical basis. First and for an elementary conguration with linear utility, it is proved that the rate of growth of investment is prone to andoscillating—convergent, sustained or unstable—motions. Second and for an environment with a linear production technology and a AK setup, the dynamics of investment is explicitly solved and it is established that the rate of growth of investment may either converge to the steady growth solution in oscillating way, diverge from that solution in a oscillating way, or even undergo permanent sustained oscillations with a periodicity of two. .ird, it is proved that no perennial .uctuations can emerge within a benchmark environment with strictly concave utilities and production technologies. On a methodological basis, few restrictions are superimposed, the arguments remain fairly general and the proofs are elementary.
    Keywords: Vintage Capital,Optimal Growth,Discrete Time
    Date: 2020–05
  19. By: Elena Falcettoni; Vegard Nygaard
    Abstract: We use an expected utility framework to examine how living standards vary across the United States and how each state's living standards have evolved over time. Our welfare measure accounts for cross-state variations in mortality, consumption, education, inequality, and cost of living. We find that per capita income is a good indicator of living standards, with a correlation of 0.80 across states. Living standards in most states, however, appear closer to those in the richest states than their difference in per capita income would suggest. Whereas high-income states benefit from higher life expectancy, consumption, and college attainment, low-income states benefit from lower cost of living. All states experienced positive welfare growth, and hence rising living standards, between 1999 and 2015. The annual welfare growth rate, however, varied from 1.38 to 3.76 percent across states due to varying gains in life expectancy, consumption, and college attainment, with life ex pectancy accounting for 50.3 percent of the variation. Finally, the growth rate of per capita income is a poor proxy for how fast living standards are rising in a particular state since the correlation between welfare growth and per capita income growth is only 0.38, and deviations are often large.
    Keywords: Expected utility; Living standards; Inequality; Cost of living; Welfare comparison; States of America; Quality of life
    JEL: D63 I31 O50 R13
    Date: 2020–05–22

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