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on Utility Models and Prospect Theory |
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Issue of 2023‒12‒18
fourteen papers chosen by |
| By: | Francesco Ruscitti; Ram Sewak Dubey; Giorgio Laguzzi |
| Abstract: | Motivated by the analysis of a general optimal portfolio selection problem, which encompasses as special cases an optimal consumption and an optimal debt-arrangement problem, we are concerned with the questions of how a personality trait like risk-perception can be formalized and whether the two objectives of utility-maximization and risk-minimization can be both achieved simultaneously. We address these questions by developing an axiomatic foundation of preferences for which utility-maximization is equivalent to minimizing a utility-based shortfall risk measure. Our axiomatization hinges on a novel axiom in decision theory, namely the risk-perception axiom. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.07269&r=upt |
| By: | Yuhki Hosoya |
| Abstract: | In this paper, we study the continuity of expected utility functions, and derive a necessary and sufficient condition for a weak order on the space of simple probabilities to have a continuous expected utility function. We also verify that almost the same condition is necessary and sufficient for a weak order on the space of probabilities with compact-support to have a continuous expected utility function. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.16806&r=upt |
| By: | Johan E. Gustafsson (University of Texas at Austin, USA. University of York, UK. IFFS, Sweden); Dean Spears (University of Texas at Austin, USA. IZA, Germany. IFFS, Sweden. GPI, Oxford University, UK); Stéphane Zuber (Université Paris 1 Panthéon-Sorbonne, CNRS, & Paris School of Economics, Centre d'Economie de la Sorbonne) |
| Abstract: | The expectation of a sum of utilities is a core criterion for evaluating policies and social welfare under variable population and social risk. Our innovation is to show that a previously unrecognized combination of weak assumptions yields general versions of this criterion, both in fixed-population and in variable-population settings. We show that two dimensions of weak dominance (over risk and individuals) characterize a social welfare function with two dimensions of additive separability. So social expected utility emerges merely from social statewise dominance (given other axioms). Moreover, additive utilitarianism, in the variable-population setting, arises from a new, weak form of individual stochastic dominance with two attractive properties: It only applies to lives certain to exist (so it does not compare life against non-existence), and it avoids prominent egalitarian objections to utilitarianism by only applying if certain correlations are preserved. Our result provides a foundation for evaluating climate change, growth, and depopulation |
| Keywords: | Social risk; variable population; utilitarianism |
| JEL: | D63 D81 |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:23016&r=upt |
| By: | Taisuke Imai; Klaus M. Schmidt |
| Abstract: | Loss aversion postulates that people prefer avoiding losses over acquiring gains of equal size. It is a central part of prospect theory and, according to Daniel Kahneman, “the most significant contribution of psychology to behavioral economics” (Kahneman, 2011, p. 300). It has powerful implications for decision theory and has been fruitfully applied in many subfields of economics. However, because the reference point is often not well defined and loss aversion interacts with other behavioral biases, there is some controversy about the concept. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1218&r=upt |
| By: | Wenyuan Wang; Kaixin Yan; Xiang Yu |
| Abstract: | This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our goal is to understand impacts of the short-selling constraint and the periodic reward structure on the long-run optimal portfolio strategy. Under logarithmic and power utilities, we first reformulate the original problem into an auxiliary one-period optimization problem. To cope with the auxiliary problem with no short-selling, the dual control problem is introduced and studied, which gives the characterization of the candidate optimal portfolio within one period. With the help of the obtained results from the auxiliary problem, the value function and the optimal constrained portfolio for the original problem with periodic evaluation over an infinite horizon can be further derived and verified, allowing us to discuss some interesting financial implications under the new performance paradigm. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.12517&r=upt |
| By: | Leonard Mushunje; David Edmund Allen |
| Abstract: | We studied the behavior and variation of utility between the two conflicting players in a closed Nash-equilibrium loop. Our modeling approach also captured the nexus between optimal premium strategizing and firm performance using the Lotka-Volterra completion model. Our model robustly modeled the two main cases, insurer-insurer and insurer-policyholder, which we accompanied by numerical examples of premium movements and their relationship to the market equilibrium point. We found that insurers with high claim exposures tend to set high premiums. The other competitors either set a competitive premium or adopt the fixed premium charge to remain in the game; otherwise, they will operate below the optimal point. We also noted an inverse link between trading premiums and claims in general insurance games due to self-interest and utility indifferences. We concluded that while an insurer aims to charge high premiums to enjoy more, policyholders are willing to avoid these charges by paying less. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.10917&r=upt |
| By: | Sascha Desmettre; Sebastian Merkel; Annalena Mickel; Alexander Steinicke |
| Abstract: | We study and solve the worst-case optimal portfolio problem as pioneered by Korn and Wilmott (2002) of an investor with logarithmic preferences facing the possibility of a market crash with stochastic market coefficients by enhancing the martingale approach developed by Seifried in 2010. With the help of backward stochastic differential equations (BSDEs), we are able to characterize the resulting indifference optimal strategies in a fairly general setting. We also deal with the question of existence of those indifference strategies for market models with an unbounded market price of risk. We therefore solve the corresponding BSDEs via solving their associated PDEs using a utility crash-exposure transformation. Our approach is subsequently demonstrated for Heston's stochastic volatility model, Bates' stochastic volatility model including jumps, and Kim-Omberg's model for a stochastic excess return. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.10021&r=upt |
| By: | Fedor Slepov (National Research University Higher School of Economics); Sergey Kokovin (National Research University Higher School of Economics) |
| Abstract: | This paper develops a modeling technique of “attainable profit” functions, applying it to two models of monopolistic competition. First, it revisits the Krugman’s classical trade model in the most general form: several asymmetric countries and non-specified additive utility functions. We establish the weakest conditions on utilities, sufficient for the existence of equilibria. These conditions are also necessary under symmetric preferences. Equilibrium uniqueness is proved only for the case of two countries. Second, we study another, “indirectly additive” trade model (Bertoletti and Etro, 2015), and establish weak conditions on non-specified indirect utilities for the existence of equilibria in several asymmetric countries. |
| Keywords: | international trade, monopolistic competition, variable elasticity of substitution, variable markups, existence of equilibria, attainable profits |
| JEL: | F12 L13 D43 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:262/ec/2023&r=upt |
| By: | Breitmoser, Yves (Universität Bielefeld); Valasek, Justin (Dept. of Economics, Norwegian School of Economics and Business Administration) |
| Abstract: | We report on the results of an experiment designed to disentangle behavioral biases in information aggregation of committees. Subjects get private signals about the state of world, send binary messages, and finally vote under either majority or unanimity rules. Committee decisions are significantly more efficient than predicted by Bayesian equilibrium even with lying aversion. Messages are truthful, subjects correctly anticipate the truthfulness (contradicting limited depth of reasoning), but strikingly overestimate their pivotality when voting (contradicting plain lying aversion). That is, committees are efficient because members message truthfully and vote non-strategically. We show that all facets of behavior are predicted by overreaction, subjects overshooting in Bayesian updating, which implies that subjects exaggerate the importance of truthful messages and sincere voting. A simple one-parameteric generalization of quantal response equilibrium capturing overreaction covers 87 percent of observed noise. |
| Keywords: | committees; incomplete information; cheap talk; information aggregation; laboratory experiment; Bayesian updating; lying aversion; limited depth of reasoning |
| JEL: | C90 D71 D72 |
| Date: | 2023–11–21 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhheco:2023_018&r=upt |
| By: | Zongxia Liang; Jianming Xia; Fengyi Yuan |
| Abstract: | This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification theorems for equilibrium strategies, accommodating both random market coefficients and incomplete markets. We derive the first-order condition (FOC) for the equilibrium strategies, using a notion of functional derivatives with respect to probability distributions. Then, with the help of the FOC we obtain the equilibrium strategies in closed form for two classes of implicitly defined preferences: CRRA and CARA betweenness preferences, with deterministic market coefficients. Finally, to show applications of our theoretical results to problems with random market coefficients, we examine the weighted utility. We reveal that the equilibrium strategy can be described by a coupled system of Quadratic Backward Stochastic Differential Equations (QBSDEs). The well-posedness of this system is generally open but is established under the special structures of our problem. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.06745&r=upt |
| By: | Federico A. Bugni; Yulong Wang |
| Abstract: | This paper considers inference in first-price and second-price sealed-bid auctions with a large number of symmetric bidders having independent private values. Given the abundance of bidders in each auction, we propose an asymptotic framework in which the number of bidders diverges while the number of auctions remains fixed. This framework allows us to perform asymptotically exact inference on key model features using only transaction price data. Specifically, we examine inference on the expected utility of the auction winner, the expected revenue of the seller, and the tail properties of the valuation distribution. Simulations confirm the accuracy of our inference methods in finite samples. Finally, we also apply them to Hong Kong car license auction data. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.09972&r=upt |
| By: | Maximilian Blesch (HU Berlin, DIW Berlin); Philipp Eisenhauer (Amazon) |
| Abstract: | Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model’s implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision problem to misspecification, and ultimately leads to post-decision disappointment. Using statistical decision theory, we develop a framework to explore, evaluate, and optimize robust decision rules that explicitly account for estimation uncertainty. We show how to operationalize our analysis by studying robust decisions in a stochastic dynamic investment model in which a decision-maker directly accounts for uncertainty in the model’s transition dynamics. |
| Keywords: | decision-making under uncertainty; robust Markov decision process; |
| JEL: | D81 C44 D25 |
| Date: | 2023–11–22 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:463&r=upt |
| By: | Davide Radi; Laura Gardini |
| Abstract: | The global dynamics is investigated for a duopoly game where the perfect foresight hypothesis is relaxed and firms are worst-case maximizers. Overlooking the degree of product substitutability as well as the sensitivity of price to quantity, the unique and globally stable Cournot-Nash equilibrium of the complete-information duopoly game, loses stability when firms are not aware if they are playing a duopoly game, as it is, or an oligopoly game with more than two competitors. This finding resembles Theocharis' condition for the stability of the Cournot-Nash equilibrium in oligopolies without uncertainty. As opposed to complete-information oligopoly games, coexisting attractors, disconnected basins of attractions and chaotic dynamics emerge when the Cournot-Nash equilibrium loses stability. This difference in the global dynamics is due to the nonlinearities introduced by the worst-case approach to uncertainty, which mirror in bimodal best-reply functions. Conducted with techniques that require a symmetric setting of the game, the investigation of the dynamics reveals that a chaotic regime prevents firms from being ambiguity averse, that is, firms are worst-case maximizers only in the quantity-expectation space. Therefore, chaotic dynamics are the result and at the same time the source of profit uncertainty. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.11366&r=upt |
| By: | Harvey Lederman |
| Abstract: | This paper introduces the axiom of Negative Dominance, stating that if a lottery $f$ is strictly preferred to a lottery $g$, then some outcome in the support of $f$ is strictly preferred to some outcome in the support of $g$. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.08471&r=upt |