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on Utility Models and Prospect Theory |
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Issue of 2019‒10‒21
sixteen papers chosen by |
| By: | Stark, Oded (University of Bonn); Budzinski, Wiktor (University of Warsaw); Jakubek, Marcin (Institute of Economics, Polish Academy of Sciences) |
| Abstract: | Assuming that an individual's rank in the wealth distribution is the only factor determining the individual's wellbeing, we analyze the individual's risk preferences in relation to gaining or losing rank, rather than the individual’s risk preferences towards gaining or losing absolute wealth. We show that in this characterization of preferences, a high-ranked individual is more willing than a low-ranked individual to take risks that can provide him with a rise in rank: relative risk aversion with respect to rank in the wealth distribution is a decreasing function of rank. This result is robust to incorporating (the level of) absolute wealth in the individual's utility function. |
| Keywords: | rank in the wealth distribution, rank-based utility, variation in risk-taking behavior, relative risk aversion |
| JEL: | D01 D31 D81 G32 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp12637&r=all |
| By: | Stark, Oded; Budzinski, Wiktor; Jakubek, Marcin |
| Abstract: | Assuming that an individual's rank in the wealth distribution is the only factor determining the individual's wellbeing, we analyze the individual's risk preferences in relation to gaining or losing rank, rather than the individual's risk preferences towards gaining or losing absolute wealth. We show that in this characterization of preferences, a high-ranked individual is more willing than a low-ranked individual to take risks that can provide him with a rise in rank: relative risk aversion with respect to rank in the wealth distribution is a decreasing function of rank. This result is robust to incorporating (the level of) absolute wealth in the individual's utility function. |
| Keywords: | Rank in the wealth distribution,Rank-based utility,Variation in risk-takingbehavior,Relative risk aversion |
| JEL: | D01 D31 D81 G32 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:tuewef:123&r=all |
| By: | Alain Marciano (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier); Alessandro Melcarne (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique); Giovanni Ramello (Dipartimento di scienze giuridiche ed economiche, Universita degli studi del piemonte orientale - Universita degli studi del piemonte orienta) |
| Abstract: | Richard Posner's "What Do Judges and Justices Maximize?" (1993a) is not, as usually believed, the first analysis of judges' behaviors made by using the assumption that judges are rational and maximize a utility function. It arrived at the end of a rather long process. This paper recounts the history of this process, from the "birth" of law and economics in the 1960s to 1993. We show that economic analyses of judge behavior were introduced in the early 1970s under the pen of Posner. At that time, rationality was not modeled in terms of utility maximization. Utility maximization came later. We also show that rationality and incentives were introduced to explain the efficiency of Common Law. Around this theme, a controversy took place that led Posner, and other economists, to postpone their analysis of judicial behavior until the 1990s. By then, the situation had changed. New and conclusive evidence of judges' utility maximizing behavior demanded for a general theory to be expressed. In addition, the context was favorable to Chicago economists. It was time for Posner to publish his article. |
| Keywords: | Self-interest,Utility Maximization,Judges,Judicial decision making,Rationality |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-02306821&r=all |
| By: | Ljudmila A. Bordag |
| Abstract: | We study an optimization problem for a portfolio with a risk-free, a liquid risky, and an illiquid asset which is sold in an exogenous random moment of time with a prescribed liquidation time distribution. Problems of such type lead to three dimensional nonlinear partial differential equations (PDEs) on the value function. We study the optimization problem with a utility function of a CARA type, i.e. with negative and positive exponential utility functions (EXPn and EXPp). It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure: in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity. In our previous papers devoted to the optimization problem with a HARA and LOG utility functions we proved that also the corresponding analytical and Lie algebraic structures are connected with the same limiting procedure. In this paper we show that the case of EXPn utility function differs from the case of the HARA utility and is not connected to the HARA case by the limiting procedure. We carry out the Lie group analysis of the PDEs for the cases EXPn and EXPp utility functions and proved that they are connected by a one-to-one analytical substitution and are identical from the economical, analytical or Lie algebraic point of view. The complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra. We prove that in one case the invariant reduction is consistent with the boundary condition. We can use the reduced two dimensional PDE to study the properties of the optimal solution and the investment - consumption strategies. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.07417&r=all |
| By: | Ben-Zhang Yang; Xiaoping Lu; Guiyuan Ma; Song-Ping Zhu |
| Abstract: | This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without derivative trading. To illustrate the effects of ambiguity, we compare our optimal robust strategy with some strategies that ignore the information of uncertainty, and provide the corresponding welfare analysis. The effects of derivative trading to the optimal portfolio selection are also discussed by considering alternative strategies. Our study is further extended to the cases with jump risks in asset price and correlated volatility factors, respectively. Numerical experiments are provided to demonstrate the behavior of the optimal portfolio and utility loss. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.06872&r=all |
| By: | Matteo Brachetta; Claudia Ceci |
| Abstract: | We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton-Jacobi-Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.05999&r=all |
| By: | Marques, Jorge; Pascoal, Rui |
| Abstract: | In the neoclassical theory, the economic value of a good is determined by the benefit that an individual consumer attributes to the last ("marginal") unit consumed. Marginal analysis was introduced to the theory of value by William Jevons, Carl Menger and Léon Walras, the founders of marginalism. Since the so-called “marginalist revolution” of the 1870s, differential (or infinitesimal) calculus has been applied to the mathematical modelling of economic theories. Our goal is to present some consumer behavior models, their advantages and limitations, using the methodology of economic science. It should be emphasized that each (re)formulation is based on different economic principles: diminishing marginal utility, diminishing marginal rate of substitution and weak axiom of revealed preference. |
| Keywords: | Marginal analysis, consumer behavior models, diminishing marginal rate of substitution, weak axiom of revealed preference |
| JEL: | C02 D03 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96442&r=all |
| By: | Tim Leung; Yang Zhou |
| Abstract: | We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures trading strategy. This leads to the analysis of the associated system of Hamilton-Jacobi-Bellman (HJB) equations, which are reduced to a system of linear ODEs. We apply our stochastic framework to two models, namely, the Regime-Switching Geometric Brownian Motion (RS-GBM) model and Regime-Switching Exponential Ornstein-Uhlenbeck (RS-XOU) model. Numerical examples are provided to illustrate the investor's optimal futures positions and portfolio value across market regimes. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.06432&r=all |
| By: | Doval, Laura; Skreta, Vasiliki |
| Abstract: | We show that posted prices are the optimal mechanism to sell a durable good to a privately informed buyer when the seller has limited commitment in an infinite horizon setting. We provide a methodology for mechanism design with limited commitment and transferable utility. Whereas in the case of commitment, subject to the buyer's truthtelling and participation constraints, the seller's problem is a decision problem, in the case of limited commitment, the seller's problem corresponds to an intrapersonal game, where different "incarnations" of the seller represent the different beliefs he may have about the buyer's valuation. |
| Keywords: | information design; intrapersonal equilibrium; Limited Commitment; mechanism design; posted price; self-generation |
| JEL: | D84 D86 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13967&r=all |
| By: | Andrew Papanicolaou; Shiva Chandra |
| Abstract: | We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $\epsilon$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of $\sqrt\epsilon$. In this paper we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.06463&r=all |
| By: | Jos\'e Cl\'audio do Nascimento |
| Abstract: | This paper shows that the $q$-exponential function rationally evaluate the time discounting. When we consider two processes of wealth accumulation with different frequencies, then the discount rate and the relative frequency between them are essentials to choose the best process. In this context, the exponential discounting is a particular case, where one of the processes has a much higher frequency related to the other. In addition, one can note that some behaviors observed empirically in decision makers, such as subadditivity, magnitude effect, and preference reversal, are consistent with processes which have a low relative frequency. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.05209&r=all |
| By: | Antonio Cutanda (Department of Economic Analysis, University of Valencia, Avda. dels Tarongers s/n, 46022 Valencia (Spain).); Juan A. Sanchis Llopis (Department of Economic Structure, University of Valencia, Avda. dels Tarongers s/n, 46022 Valencia (Spain).) |
| Abstract: | In this paper we test the three first-order conditions of an intertemporal optimization model for a representative individual who chooses simultaneously for her level of consumption and leisure, assuming a separable utility function. We estimate these first order conditions separately and jointly using a Spanish pseudo-panel data set built by combining the Family Expenditure Survey and the Labour Survey for Spain over the period 1987-1997. Our results confirm previous empirical evidence as regards the elasticity of intertemporal substitution for consumption, that we estimate around 0.4/0.5, and provide an estimate for the leisure intertemporal elasticity around 0.2/0.3. Finally, we provide further evidence controlling for human capital. This allows checking that the model ignoring human capital produces biased estimates for the elasticity of intertemporal substitution for leisure. |
| Keywords: | Euler equation, Instrumental variables, Intertemporal Substitution, Panel data |
| JEL: | C33 C36 E21 E24 J22 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:eec:wpaper:1909&r=all |
| By: | Hitoshi Shigeoka |
| Abstract: | Risk preferences play a fundamental role in individuals’ economic decision-making. We examine whether the historical macroeconomic environment shapes individuals’ willingness to take risks. Using nationally representative samples from Japan and exploiting regional variation in economic conditions, we find that men who experienced severe economic conditions in youth are more risk averse in adulthood and the effect is long-lasting. In addition, those men are less likely to be self-employed and they have longer tenure, which are consistent with elevated risk aversion. This study highlights the importance of experience at a critical period of life on the formation of risk preferences. |
| JEL: | D81 J24 Z13 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26352&r=all |
| By: | Valentin Haddad; David A. Sraer |
| Abstract: | Banks' balance-sheet exposure to fluctuations in interest rates strongly forecasts excess Treasury bond returns. This result is consistent with optimal risk management, a banking counterpart to the household Euler equation. In equilibrium, the bond risk premium compensates banks for bearing fluctuations in interest rates. When banks' exposure to interest rate risk increases, the price of this risk simultaneously rises. We present a collection of empirical observations supporting this view, but also discuss several challenges to this interpretation. |
| JEL: | G0 G12 G21 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26369&r=all |
| By: | Bell, Clive (Heidelberg University); Gersbach, Hans (ETH Zurich); Komarov, Evgenij (ETH Zurich) |
| Abstract: | This paper analyses the effects of disease and war on the accumulation of human and physical capital. We employ an overlapping-generations frame-work in which young adults, confronted with such hazards and motivated by old-age provision and altruism, make decisions about investments in schooling and reproducible capital. A poverty trap exists for a wide range of stationary war losses and premature adult mortality. If parents are altruistic and their sub-utility function for own consumption is more concave than that for the children's human capital, the only possible steady-state growth path involves full education. Otherwise, steady-state paths with incompletely educated children may exist, some of them stationary ones. We also examine, analytically and with numerical examples, a growing economy's robustness in a stochastic environment. The initial boundary conditions have a strong influence on outcomes in response to a limited sequence of destructive shocks. |
| Keywords: | premature mortality, capital accumulation and destruction, steady states, poverty traps, overlapping generations |
| JEL: | D91 E13 I15 I25 O11 O41 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp12680&r=all |
| By: | Muringai, Violet; Fan, Xiaoli; Goddard, Ellen |
| Abstract: | In 2016, the second-generation genetically modified (GM) potatoes were approved for production and sale in Canada. In this study, we analyze how consumer acceptance of GM potatoes are affected by various factors including the trait introduced (i.e., the product benefits) by using genetic technologies, the type of breeding technology used, and the developer of the potato with any technology. We conduct an online survey and use a stated choice experiment to collect data on consumer acceptance of GM and gene-edited potatoes in Canada. Random utility models are used to analyze the economic value consumers place on the attributes of the GM and gene-edited potatoes. Our results show that consumers are willing to pay more for a health attribute (reduced acrylamide produced when potatoes are fried) as compared to environmental benefits. Respondents in general need to face discounted prices to buy potatoes created by either gene editing or GM (both transgenic and cisgenic/intragenic) technologies. However, consumers are more accepting of the gene editing technology than GM technologies. Our results also show that government is the most preferred developer of the potatoes. Results from this study can help policymakers design better information policies to improve consumer acceptance of gene-edited and GM potatoes. |
| Keywords: | Agricultural and Food Policy, Crop Production/Industries, Food Consumption/Nutrition/Food Safety |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaacwp:294164&r=all |