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on Utility Models and Prospect Theory |
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Issue of 2023‒05‒15
eighteen papers chosen by |
| By: | Yunhong Li; Zuo Quan Xu; Xun Yu Zhou |
| Abstract: | We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution, hence an ``intractable claim''. In view of the lack of necessary information about the claim, we consider a robust formulation to maximize her utility in the worst scenario. We apply the quantile formulation to solve the problem, expressing the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations. In the case of an exponential utility, the problem reduces to a (non-robust) rank--dependent utility maximization with probability distortion whose solution is available in the literature. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.06938&r=upt |
| By: | Christopher P. Chambers; Georgios Gerasimou |
| Abstract: | Although portfolio diversification is the typical strategy followed by risk-averse investors, extreme portfolios that allocate all funds to a single asset/state of the world are common too. Such asset-demand behavior is compatible with risk-averse subjective expected utility maximization under beliefs that assign a strictly positive probability to every state. We show that whenever finitely many extreme asset demands are rationalizable in this way under such beliefs, they are simultaneously rationalizable under the same beliefs by: (i) constant absolute risk aversion; decreasing absolute risk aversion/increasing relative risk aversion (DARA/IRRA); risk-neutral; and ris-kseeking utility indices at all wealth levels; (ii) a distinct class of DARA/IRRA utility indices at some strictly positive fixed initial wealth; and (iii) decreasing relative risk aversion utility indices under bounded wealth. We also show that, in such situations, the observable data allow for sharp bounds to be given for the relevant parameters in each of the above classes of risk-averse preferences. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.08059&r=upt |
| By: | Yingting Miao; Qiang Zhang |
| Abstract: | Transaction costs play a critical role in asset allocation and consumption strategies in portfolio management. We apply the methods of dynamic programming and singular perturbation expansion to derive the closed-form leading solutions to this problem for small transaction costs with arbitrary transaction cost structure by maximizing the expected CRRA (constant relative risk aversion) utility function for this problem. We also discuss in detail the case which consists of both fixed and proportional transaction costs. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.07672&r=upt |
| By: | Mohajan, Devajit; Mohajan, Haradhan |
| Abstract: | In this study sensitivity analysis among Lagrange multipliers and commodity coupons is discussed with detailed mathematical analysis. In economics, utility maximization method is essential for increasing sustainable production and profit maximization. Two types of constraints, such as budget constraint, and coupon constraint are used to operate sensitivity analysis; consequently, two Lagrange multipliers are applied for the detailed mathematical analysis. |
| Keywords: | Lagrange multipliers, commodity coupon, sensitivity analysis, utility maximization |
| JEL: | C3 C53 C58 C61 C67 I31 |
| Date: | 2023–01–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:117077&r=upt |
| By: | Tomas E. Caravello (Massachusetts Institute of Technology); John Driffill (Yale-NUS); Turalay Kenc (University of Cambridge); Martin Sola (Universidad Torcuato di Tella) |
| Abstract: | We develop and estimate a consumption-based asset pricing model that assumes recursive utility using historical US financial data, allowing for regime changes, priced regime risk, and intrinsic bubbles. We also estimate several restricted versions which include only a subset of these features. We find that switching risk is an essential component of the equity risk premium, explaining up to fifty percent of it. Furthermore, a model which does not take this into account would overestimate the degree of risk aversion of the public, mistakenly assigning the observed risk premium to high-risk aversion instead of priced regime-switching. Intrinsic bubbles are not crucial in explaining the risk premia, but they substantially improve the model’s fit at the end of the sample. |
| Keywords: | Equity Risk Premium; Macroeconomic Risk; Stochastic Differential Utility; Markov Chain; Intrinsic Bubbles |
| JEL: | G00 G12 E44 C32 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:237&r=upt |
| By: | David Lowing (Kyushu University); Makoto Yokoo (Kyushu University) |
| Abstract: | A Sharing value for transferable utility games distributes the Harsanyi dividend of each coalition among the players in the coalition's support. Such distribution is done according to a certain sharing system that determines the Sharing value. In this paper, we extend Sharing values to multi-choice games. Multi-choice games are a generalization of transferable utility games in which players have several activity levels. Unlike in transferable utility games, there is no straightforward way to interpret the support of a coalition in a multi-choice game. This makes it more tedious to distribute the Harsanyi dividend of a multi-choice coalition. We consider three possible interpretations of the support of a multi-choice coalition. Based on these interpretations, we derive three families of Sharing values for multi-choice games. To conduct this study, we discuss novel and classical axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these families of values. |
| Keywords: | Multi-choice games, Sharing values, Harsanyi set |
| Date: | 2023–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04018735&r=upt |
| By: | Junlong Feng; Sokbae Lee |
| Abstract: | We introduce a novel framework for individual-level welfare analysis. It builds on a parametric model for continuous demand with a quasilinear utility function, allowing for unobserved individual-product-level preference shocks. We obtain bounds on the individual-level consumer welfare loss at any confidence level due to a hypothetical price increase, solving a scalable optimization problem constrained by a new confidence set under an independence restriction. This confidence set is computationally simple, robust to weak instruments and nonlinearity, and may have applications beyond welfare analysis. Monte Carlo simulations and two empirical applications on gasoline and food demand demonstrate the effectiveness of our method. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.01921&r=upt |
| By: | Masaaki Fujii; Masashi Sekine |
| Abstract: | In this paper, we study a problem of equilibrium price formation among many investors with exponential utility. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to a novel mean-field backward stochastic differential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.07108&r=upt |
| By: | Massimo Marinacci; Giulio Principi; Lorenzo Stanca |
| Abstract: | We illustrate the strong implications of recursivity, a standard assumption in dynamic environments, on attitudes toward uncertainty. In intertemporal consumption choice problems, recursivity always implies constant absolute ambiguity aversion (CAAA) when applying the standard dynamic extension of monotonicity. Our analysis also yields a functional equation called "generalized rectangularity", as it generalizes the standard notion of rectangularity for recursive maxmin preferences to general certainty equivalents. Our results highlight that if uncertainty aversion is modeled as a form of convexity of preferences, recursivity limits us to only recursive variational preferences. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.06830&r=upt |
| By: | Matthew Kovach; Gerelt Tserenjigmid |
| Abstract: | We propose a generalization of Quantal Response Equilibrium (QRE) built on a simple premise: some actions are more focal than others. In our model, which we call the Focal Quantal Response Equilibrium (Focal QRE), each player plays a stochastic version of Nash equilibrium as in the QRE, but some strategies are focal and thus are chosen relatively more frequently than other strategies after accounting for expected utilities. The Focal QRE is able to systemically account for various forms of bounded rationality of players, especially regret-aversion, salience, or limited consideration. The Focal QRE is also useful to explain observed heterogeneity of bounded rationality of players across different games. We show that regret-based focal sets perform relatively well at predicting strategies that are chosen more frequently relative to their expected utilities. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.00438&r=upt |
| By: | Hannah Zillessen |
| Abstract: | In most Western countries, migrants hold significantly less wealth than natives. Migrants also face significantly more uncertainty about their future. This paper examines the central role of uncertainty over citizenship prospects and future location in explaining their saving choices. Exploiting quasi-experimental variation and panel data from Germany, I show that migrants with a right to citizenship save as much as comparable natives, while migrants without this right save 30% less. This unexplained gap is closed completely when migrants in the latter group gain access to citizenship. The effect is not driven by changes in resources, but rather willingness to save. While standard theory predicts that saving increases in uncertainty, I show that the effect can reverse if utility is state-dependent, malleable, or resources are not equally accessible across states. I build a life-cycle saving model with uncertain retirement location and heterogeneous country preferences. The model shows that agents can have a “preparatory saving motive” that decreases in uncertainty. I confirm the importance of this novel motive empirically, showing that migrants become significantly more likely to invest in illiquid assets if they gain certainty about their right to stay. |
| Date: | 2022–11–10 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:1008&r=upt |
| By: | Lepinteur, Anthony (University of Luxembourg); Borga, Liyousew G. (Luxembourg Institute of Health); Clark, Andrew E. (Paris School of Economics); Vögele, Claus (University of Luxembourg); D'Ambrosio, Conchita (University of Luxembourg) |
| Abstract: | We here investigate the role of risk aversion in COVID-19 vaccine hesitancy. The theoretical effect is ambiguous, as both COVID-19 infection and vaccination side-effects involve probabilistic elements. In large-scale data covering five European countries, we find that vaccine hesitancy falls with risk aversion, so that COVID-19 infection is perceived as involving greater risk than is vaccination. |
| Keywords: | risk aversion, COVID-19, vaccine hesitancy |
| JEL: | I12 D81 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp16084&r=upt |
| By: | Yuling Yan; Weijie J. Su; Jianqing Fan |
| Abstract: | In 2023, the International Conference on Machine Learning (ICML) required authors with multiple submissions to rank their submissions based on perceived quality. In this paper, we aim to employ these author-specified rankings to enhance peer review in machine learning and artificial intelligence conferences by extending the Isotonic Mechanism (Su, 2021, 2022) to exponential family distributions. This mechanism generates adjusted scores closely align with the original scores while adhering to author-specified rankings. Despite its applicability to a broad spectrum of exponential family distributions, this mechanism's implementation does not necessitate knowledge of the specific distribution form. We demonstrate that an author is incentivized to provide accurate rankings when her utility takes the form of a convex additive function of the adjusted review scores. For a certain subclass of exponential family distributions, we prove that the author reports truthfully only if the question involves only pairwise comparisons between her submissions, thus indicating the optimality of ranking in truthful information elicitation. Lastly, we show that the adjusted scores improve dramatically the accuracy of the original scores and achieve nearly minimax optimality for estimating the true scores with statistical consistecy when true scores have bounded total variation. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.11160&r=upt |
| By: | Nicolás Salamanca (Melbourne Institute, University of Melbourne); Buly A. Cardak (La Trobe Business School, La Trobe University); Edwin Ip (Department of Economics, University of Exeter); Joe Vecci (Department of Economics, University of Gothenburg) |
| Abstract: | Time-stability of preferences is a crucial assumption in economics. We develop a novel test-retest method to examine the stability of risk preferences over time, while quantifying the importance of both idiosyncratic shocks and measurement error. Using eight large, representative datasets from developing and developed countries, we find risk preferences to be unstable in developing countries. In contrast, they are very stable in developed countries, except for low-income individuals in the U.S.. We discuss the important implications of these findings for policies and research. |
| Keywords: | risk preferences, stability, economic development |
| JEL: | D01 D81 O10 C18 |
| Date: | 2023–04–17 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:2305&r=upt |
| By: | John Duffy; Janet Hua Jiang; Huan Xie |
| Abstract: | We study indefinitely lived assets in experimental markets and find that the traded prices of these assets are, on average, about 40% of the risk-neutral fundamental value. Neither uncertainty about the value of total dividend payments nor horizon uncertainty about the duration of trade can account for this low traded price. An Epstein and Zin (1989) recursive preference specification that models the dynamic realization of dividend payments and incorporates risk preferences can rationalize the low traded price observed in our indefinitely lived asset market. |
| Keywords: | Asset pricing; Financial markets |
| JEL: | C92 D81 G12 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:23-25&r=upt |
| By: | Nicholas Ingwersen; Elizabeth Frankenberg; Duncan Thomas |
| Abstract: | The impact of exposure to a major unanticipated natural disaster on the evolution of survivors’ attitudes toward risk is examined, exploiting plausibly exogenous variation in exposure to the 2004 Indian Ocean tsunami in combination with rich population-representative longitudinal survey data spanning the five years after the tsunami. Respondents chose among pairs of hypothetical income streams. Those directly exposed to the tsunami made choices consistent with greater willingness to take on risk relative to those not directly exposed to the tsunami. These differences are short-lived: starting a year later, there is no evidence of differences in willingness to take on risk between the two groups. These conclusions hold for tsunami-related exposures measured at the individual and community level. Apparently, tsunami survivors were inclined to assume greater financial risk in the short-term while rebuilding their lives after the disaster. |
| JEL: | D12 D81 O12 Q54 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31102&r=upt |
| By: | Masaaki Fujii (Faculty of Economics, The University of Tokyo); Masashi Sekine (Faculty of Economics, The University of Tokyo) |
| Abstract: | In this paper, we study a problem of equilibrium price formation among many investors with exponential utility. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to a novel mean-field backward stochastic dierential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2023cf1210&r=upt |
| By: | Ali Lazrak; Jianfeng Zhang |
| Abstract: | We study how decentralized utility transfer promises affect collective decision-making by voting. Committee members with varying levels of support and opposition for an efficient reform can make enforceable promises before voting. An equilibrium requires stability and minimal promises. Equilibrium promises exist and are indeterminate, but do share several key characteristics. Equilibria require transfer promises from high to low intensity members and result in enacting the reform. When reform supporters lack sufficient voting power, promises must reach across the aisle. Even if the coalition of reform supporters is decisive, promises must preclude the least enthusiastic supporters of the reform from being enticed to overturn the decision. In that case, equilibrium promises do not need to reach across the aisle. We also discuss a finite sequence of promises that achieve an equilibrium. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.08008&r=upt |