
on Utility Models and Prospect Theory 
Issue of 2021‒07‒26
twentytwo papers chosen by Alexander Harin Modern University for the Humanities 
By:  Zongxia Liang; Yang Liu; Ming Ma 
Abstract:  We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utility, including many nonstandard utilities as examples. A typical application is the composition of an HARA preference and a piecewise linear payoff in hedge fund management. We derive a unified closedform formula of the optimal portfolio, which is a fourterm division. The formula has clear economic meanings, reflecting the behavior of risk aversion, risk seeking, loss aversion and firstorder risk aversion. One main finding is that risktaking behaviors are greatly increased by nonconcavity and reduced by nondifferentiability. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.06460&r= 
By:  Jing Guo; Xue Dong He 
Abstract:  We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses. We also study the utility process in this generalized model with constant elasticity of intertemporal substitution and relative risk aversion degree, and with infinite time horizon. In a specific, finitestate Markovian setting, we prove that the utility process uniquely exists when the agent derives nonnegative gainloss utility, and that it can be nonexistent or nonunique otherwise. Moreover, we prove that the utility process, when it uniquely exists, can be computed by starting from any initial guess and applying the recursive equation that defines the utility process repeatedly. We then consider a portfolio selection problem with gainloss utility and solve it by proving that the corresponding dynamic programming equation has a unique solution. Finally, we extend certain previous results to the case in which the state space is infinite. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.05163&r= 
By:  Andrea Loi; Stefano Matta 
Abstract:  We study the connection between risk aversion, number of consumers and uniqueness of equilibrium. We consider an economy with two goods and $c$ impatience types, where each type has additive separable preferences with HARA Bernoulli utility function, $u_H(x):=\frac{\gamma}{1\gamma}(b+\frac{a}{\gamma}x)^{1\gamma}$. We show that if $\gamma\in (1, \frac{c}{c1}]$, the equilibrium is unique. Moreover, the methods used, involving Newton's symmetric polynomials and Descartes' rule of signs, enable us to offer new sufficient conditions for uniqueness in a closedform expression highlighting the role played by endowments, patience and specific HARA parameters. Finally new necessary and sufficient conditions in ensuring uniqueness are derived for the particular case of CRRA Bernoulli utility functions with $\gamma =3$. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01947&r= 
By:  Xiaoqing Liang; Ruodu Wang; Virginia Young 
Abstract:  In this paper, we study an optimal insurance problem for a riskaverse individual who seeks to maximize the rankdependent expected utility (RDEU) of her terminal wealth, and insurance is priced via a general distortiondeviation premium principle. We prove necessary and sufficient conditions satisfied by the optimal solution and consider three ambiguity orders to further determine the optimal indemnity. Finally, we analyze examples under three distortiondeviation premium principles to explore the specific conditions under which no insurance or deductible insurance is optimal. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.02656&r= 
By:  Denizalp Goktas; Enrique Areyan Viqueira; Amy Greenwald 
Abstract:  In this paper, we bring consumer theory to bear in the analysis of Fisher markets whose buyers have arbitrary continuous, concave, homogeneous (CCH) utility functions representing locally nonsatiated preferences. The main tools we use are the dual concepts of expenditure minimization and indirect utility maximization. First, we use expenditure functions to construct a new convex program whose dual, like the dual of the EisenbergGale program, characterizes the equilibrium prices of CCH Fisher markets. We then prove that the subdifferential of the dual of our convex program is equal to the negative excess demand in the associated market, which makes generalized gradient descent equivalent to computing equilibrium prices via t\^atonnement. Finally, we use our novel characterization of equilibrium prices via expenditure functions to show that a discrete t\^atonnement process converges at a rate of $O\left(\frac{1}{t}\right)$ in Fisher markets with continuous, strictly concave, homogeneous (CSCH) utility functions  a class of utility functions beyond the class of CES utility functions, the largest class for which convergence results were previously known. CSCH Fisher markets include nested and mixed CES Fisher markets, thus providing a meaningful expansion of the space of Fisher markets that is solvable via t\^atonnement. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.08153&r= 
By:  Erhan Bayraktar; Christoph Czichowsky; Leonid Dolinskyi; Yan Dolinsky 
Abstract:  The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. Surprisingly, up to date, there are no results related to the uniqueness of the optimal trading strategy. The proof of the uniqueness is heavily based on the dual approach which was developed recently in [6,7,8]. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01568&r= 
By:  Kunal Pattanayak; Vikram Krishnamurthy 
Abstract:  This paper establishes the equivalence between Bayesian revealed preference and classical revealed preference with nonlinear budget constraints. Classical revealed preference tests for utility maximization given known budget constraints. Bayesian revealed preference tests for costly information acquisition given a utility function. Our main result shows that the key theorem in Caplin and Dean (2015) on Bayesian revealed preference is equivalent to Afriattype feasibility inequalities for general (nonlinear) budget sets. Our second result exploits this equivalence of classical and Bayesian revealed preference to construct a monotone convex information acquisition cost from decision maker's data in Bayesian revealed preference 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.14486&r= 
By:  Thomas Knispel; Roger J. A. Laeven; Gregor Svindland 
Abstract:  We analyze the limiting behavior of the risk premium associated with the Pareto optimal risk sharing contract in an infinitely expanding pool of risks under a general class of lawinvariant risk measures encompassing rankdependent utility preferences. We show that the corresponding convergence rate is typically only $n^{1/2}$ instead of the conventional $n$, with $n$ the multiplicity of risks in the pool, depending upon the precise risk preferences. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01730&r= 
By:  Evan Piermont 
Abstract:  This paper provides a model to analyze and identify a decision maker's (DM's) hypothetical reasoning. Using this model, I show that a DM's propensity to engage in hypothetical thinking is captured exactly by her ability to recognize implications (i.e., to identify that one hypothesis implies another) and that this later relation is captured by a DM's observable behavior. Thus, this characterization both provides a concrete definition of (flawed) hypothetical reasoning and, importantly, yields a methodology to identify these judgments from standard economic data. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.15979&r= 
By:  Katia Colaneri; Alessandra Cretarola; Benedetta Salterini 
Abstract:  In this paper we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regimeswitching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.13888&r= 
By:  Cuong Le Van (IPAG Business School, CNRS  Centre National de la Recherche Scientifique, 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, CES  Centre d'économie de la Sorbonne  UP1  Université Paris 1 PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); NgocSang Pham (Métis Lab EM Normandie  EM Normandie  École de Management de Normandie, EM Normandie  École de Management de Normandie) 
Abstract:  We study the existence of equilibrium when agents' preferences may not be convex. For some specific utility functions, we provide a necessary and sufficient condition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single valued nor convex valued. 
Keywords:  general equilibrium.,Nonconvex preferences 
Date:  2021–03–23 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs03177843&r= 
By:  H\'el\`ene Halconruy 
Abstract:  In an incomplete market underpinned by the trinomial model, we consider two investors : an ordinary agent whose decisions are driven by public information and an insider who possesses from the beginning a surplus of information encoded through a random variable for which he or she knows the outcome. Through the definition of an auxiliary model based on a marked binomial process, we handle the trinomial model as a volatility one, and use the stochastic analysis and Malliavin calculus toolboxes available in that context. In particular, we connect the information drift, the drift to eliminate in order to preserve the martingale property within an initial enlargement of filtration in terms of the Malliavin derivative. We solve explicitly the agent and the insider expected logarithmic utility maximisation problems and provide a hedging formula for replicable claims. We identify the insider expected additional utility with the Shannon entropy of the extra information, and examine then the existence of arbitrage opportunities for the insider. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.15208&r= 
By:  Panagiotis Kanellopoulos; Maria Kyropoulou; Hao Zhou 
Abstract:  We study financial systems from a gametheoretic standpoint. A financial system is represented by a network, where nodes correspond to firms, and directed labeled edges correspond to debt contracts between them. The existence of cycles in the network indicates that a payment of a firm to one of its lenders might result to some incoming payment. So, if a firm cannot fully repay its debt, then the exact (partial) payments it makes to each of its creditors can affect the cash inflow back to itself. We naturally assume that the firms are interested in their financial wellbeing (utility) which is aligned with the amount of incoming payments they receive from the network. This defines a game among the firms, that can be seen as utilitymaximizing agents who can strategize over their payments. We are the first to study financial network games that arise under a natural set of payment strategies called priorityproportional payments. We investigate the existence and (in)efficiency of equilibrium strategies, under different assumptions on how the firms' utility is defined, on the types of debt contracts allowed between the firms, and on the presence of other financial features that commonly arise in practice. Surprisingly, even if all firms' strategies are fixed, the existence of a unique payment profile is not guaranteed. So, we also investigate the existence and computation of valid payment profiles for fixed payment strategies. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.06623&r= 
By:  Silvana M. Pesenti 
Abstract:  We consider the problem where a modeller conducts sensitivity analysis of a model consisting of random input factors, a corresponding random output of interest, and a baseline probability measure. The modeller seeks to understand how the model (the distribution of the input factors as well as the output) changes under a stress on the output's distribution. Specifically, for a stress on the output random variable, we derive the unique stressed distribution of the output that is closest in the Wasserstein distance to the baseline output's distribution and satisfies the stress. We further derive the stressed model, including the stressed distribution of the inputs, which can be calculated in a numerically efficient way from a set of baseline Monte Carlo samples. The proposed reverse sensitivity analysis framework is modelfree and allows for stresses on the output such as (a) the mean and variance, (b) any distortion risk measure including the ValueatRisk and ExpectedShortfall, and (c) expected utility type constraints, thus making the reverse sensitivity analysis framework suitable for risk models. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01065&r= 
By:  George M. Constantinides 
Abstract:  I estimate welfare benefits of eliminating idiosyncratic consumption shocks unrelated to the business cycle as 47.3% of household utility and benefits of eliminating idiosyncratic shocks related to the business cycle as 3.4% of utility. Estimates of the former substantially exceed earlier ones because I distinguish between idiosyncratic shocks related/unrelated to the business cycle, estimate the negative skewness of shocks, target moments of idiosyncratic shocks from householdlevel CEX data, and target market moments. Benefits of eliminating aggregate shocks are 7.7% of utility. Policy should focus on insuring idiosyncratic shocks unrelated to the business cycle, such as the death of a household’s prime wage earner and job layoffs not necessarily related to recessions. 
JEL:  D31 D52 E2 E21 E24 E32 E44 G01 G12 J6 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29009&r= 
By:  Peter A. Streufert 
Abstract:  This paper specifies an extensive form as a 5ary relation (i.e. set of quintuples) which satisfies certain abstract axioms. Each quintuple is understood to list a player, a situation (e.g. information set), a decision node, an action, and a successor node. Accordingly, the axioms are understood to specify abstract relationships between players, situations, nodes, and actions. Such an extensive form is called a "5form", and a "5form game" is defined to be a 5form together with utility functions. The paper's main result is to construct a bijection between (a) those 5form games with informationset situations and (b) $\mathbf{Gm}$ games (Streufert arXiv:2105.11398). In this sense, 5form games equivalently formulate almost all extensiveform games. An application weakens the tree axiom in the presence of the other axioms, which leads to a convenient decomposition of 5forms. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.10801&r= 
By:  Makarov, Dmitry 
Abstract:  A prominent approach to modelling ambiguity about stock return distribution is to assume that investors have multiple priors about the distribution and these priors are distributed according to a certain secondorder distribution. Realistically, investors may also have multiple priors about the secondorder distribution, thus allowing for ambiguous ambiguity. Despite a long history of debates about this idea (Reichenbach [1949], Savage [1954]), there seems to be no formal analysis of investment behavior in the presence of this feature. We develop a tractable portfolio choice framework incorporating ambiguous ambiguity, characterize analytically the optimal portfolio, and examine its properties. 
Keywords:  ambiguous ambiguity, portfolio choice, smooth ambiguity, thirdorder probabilities 
JEL:  D81 G11 
Date:  2020–06 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:108837&r= 
By:  Davis, John D. (Department of Economics Marquette University); McMaster, Robert (University of Glasgow) 
Abstract:  This paper departs from the standard abstract economics approach to health economics to develop a specifically contextualist approach to the subject emphasizing social and historical circumstances affecting health provision. Following Polanyi, it sees the economy as socially embedded and economic relationships as social relationships. The paper critically examines Grossmanâ€™s natural science utility maximization explanation of peopleâ€™s demand for health and health care, and advances an alternative social science account using a twoway analysis between micro level social relationships and the macro level organization of health in society. Three significant trends affecting the future of health systems are discussed. The paper closes with comments on the influence of psychology in the form of behavioral economics on the future development of a contextualist approach to health economics. 
Keywords:  contextualism, Polanyi, social embeddedness, Grossman, health systems, behavioral economics 
JEL:  I12 A12 A13 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:mrq:wpaper:202106&r= 
By:  Khaled Abedrabboh; Luluwah AlFagih 
Abstract:  The intermittent nature of renewable energy resources creates extra challenges in the operation and control of the electricity grid. Demand flexibility markets can help in dealing with these challenges by introducing incentives for customers to modify their demand. Marketbased demandside management (DSM) have garnered serious attention lately due to its promising capability of maintaining the balance between supply and demand, while also keeping customer satisfaction at its highest levels. Many researchers have proposed using concepts from mechanism design theory in their approaches to marketbased DSM. In this work, we provide a review of the advances in marketbased DSM using mechanism design. We provide a categorisation of the reviewed literature and evaluate the strengths and weaknesses of each design criteria. We also study the utility function formulations used in the reviewed literature and provide a critique of the proposed indirect mechanisms. We show that despite the extensiveness of the literature on this subject, there remains concerns and challenges that should be addressed for the realistic implementation of such DSM approaches. We draw conclusions from our review and discuss possible future research directions. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.14659&r= 
By:  Franz Dietrich (Centre d'Economie de la Sorbonne, Paris School of Economics); Brian Jabarian (Université Paris 1 Paris School of Economics) 
Abstract:  While ordinary decision theory focuses on empirical uncertainty, real decisionmakers also normative uncertainty: uncertainty about value itself. Normative uncertainty is comparable to (Harsanyian or Rawlsian) uncertainty in the 'original position', where one's values are unknown. A comprehensive decisiion theory must address twofold uncertainty  normative and empirical. We present a simple model of twofold uncertainty, and show that the most popular decision principle  maximising expected value ('Expectationalism')  has rival formulations, namely ExAnte Expectationalism, ExPost Expectationalism, and hybrid theories. These rival theories recommend different decisions, reasoning modes, and attitudes to risk. But they converge under an interesting (necessary and sufficient) condition 
Keywords:  normative versus empirical uncertainty; expected value theory; expectationalism; exante versus expost approach 
JEL:  D81 
Date:  2020–09 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:20015rr&r= 
By:  Benjamin Patrick Evans; Mikhail Prokopenko 
Abstract:  While game theory has been transformative for decisionmaking, the assumptions made can be overly restrictive in certain instances. In this work, we focus on some of the assumptions underlying rationality such as mutual consistency and bestresponse, and consider ways to relax these assumptions using concepts from level$k$ reasoning and quantal response equilibrium (QRE) respectively. Specifically, we provide an informationtheoretic twoparameter model that can relax both mutual consistency and bestresponse, but can recover approximations of level$k$, QRE, or typical Nash equilibrium behaviour in the limiting cases. The proposed approach is based on a recursive form of the variational free energy principle, representing selfreferential games as (pseudo) sequential decisions. Bounds in player processing abilities are captured as information costs, where future chains of reasoning are discounted, implying a hierarchy of players where lowerlevel players have fewer processing resources. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.15844&r= 
By:  Julie L. Hotchkiss; Robert E. Moore; Fernando RiosAvila 
Abstract:  This paper calculates the change in optimal labor supply and total family welfare resulting from the Tax Cuts and Jobs Act of 2017 (TCJA). We estimate labor supply elasticities for married families in the Current Population Survey from 2015 to 2017, using a joint family utility model. These elasticities are then used to simulate changes in optimal labor supply and resulting change in welfare among families with different characteristics under the new TCJA tax code. We find that optimal hours are lower postTCJA, relative to before. However, there are differences across family members and family types. Both men’s and women’s optimal hours decline with income starting in the second quintile, but the decline is more dramatic for men. Overall, all families’ welfare increased postTCJA, with the gains in welfare disproportionately benefiting the wealthy; families with any selfemployment income; families with children; and families renting, versus owning, their home. 
Keywords:  family welfare; joint labor supply; microsimulation; TCJA 
JEL:  D19 I30 J22 
Date:  2021–06–24 
URL:  http://d.repec.org/n?u=RePEc:fip:fedawp:92862&r= 