|
on Utility Models and Prospect Theory |
|
Issue of 2023‒03‒27
seventeen papers chosen by |
| By: | Mohajan, Devajit; Mohajan, Haradhan |
| Abstract: | In this article, sensitivity analysis between commodity and total budget are discussed. The property of a commodity that enables it to satisfy human wants is called utility. In economics, utility maximization method is essential for the welfare of the organizations and society. This study deals with four commodities and two constraints, such as budget constraint, and coupon constraint. In this article, 6×6 Hessian and 6×10 Jacobian are operated for the sensitivity analysis. Throughout the paper scientific method of optimization are applied. |
| Keywords: | Budget, Lagrange multipliers, sensitivity analysis, utility maximization |
| JEL: | B41 C3 C51 C53 D6 L6 L97 O21 |
| Date: | 2022–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:116495&r=upt |
| By: | Minglian Lin; Indranil SenGupta |
| Abstract: | In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation including the scaled covariances between the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.06778&r=upt |
| By: | Maria José Montoya Villalobos; Noémi Berlin |
| Abstract: | This experiment seeks to study the impact of uncertainty and attitudes towards uncertainty on charity donations. We use a modified dictator game, where the donations received by the beneficiaries (environmental NGOs) are exposed to different levels of uncertainty. We study the level of donations and elicit risk aversion, ambiguity aversion, likelihood insensitivity, and pessimism. We aim to test if different levels of uncertainty at the receiver level (risk and ambiguity) impact donations. We do not find any differences between levels of uncertainty compared to no uncertainty. We find that a ``high" level of ambiguity has a significant and negative effect on altruistic behavior compared to a risk or a``low" ambiguity environment. We also find that the effect of pessimism depends on the level of ambiguity. We find no effect of ambiguity aversion, likelihood insensitivity, and pessimism under ``low" ambiguity on altruistic behavior. Meanwhile, under ``high" ambiguity, we find a negative effect of pessimism on charitable giving. These results suggest that there is a threshold for which ambiguity and ambiguity attitudes have a negative impact on donations. |
| Keywords: | Charitable giving, uncertainty, pro-social behavior, ambiguity attitudes |
| JEL: | C91 D64 D81 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2023-8&r=upt |
| By: | Mina Montazeri; Hamed Kebriaei; Babak N. Araabi |
| Abstract: | Task allocation is a crucial process in modern systems, but it is often challenged by incomplete information about the utilities of participating agents. In this paper, we propose a new profit maximization mechanism for the task allocation problem, where the task publisher seeks an optimal incentive function to maximize its own profit and simultaneously ensure the truthful announcing of the agent's private information (type) and its participation in the task, while an autonomous agent aims at maximizing its own utility function by deciding on its participation level and announced type. Our mechanism stands out from the classical contract theory-based truthful mechanisms as it empowers agents to make their own decisions about their level of involvement, making it more practical for many real-world task allocation scenarios. It has been proven that by considering a linear form of incentive function consisting of two decision functions for the task publisher the mechanism's goals are met. The proposed truthful mechanism is initially modeled as a non-convex functional optimization with the double continuum of constraints, nevertheless, we demonstrate that by deriving an equivalent form of the incentive constraints, it can be reformulated as a tractable convex optimal control problem. Further, we propose a numerical algorithm to obtain the solution. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.05677&r=upt |
| By: | Guohui Guan; Zongxia Liang; Yi Xia |
| Abstract: | This paper investigates the optimal management of an aggregated defined benefit pension plan in a stochastic environment. The interest rate follows the Ornstein-Uhlenbeck model, the benefits follow the geometric Brownian motion while the contribution rate is determined by the spread method of fund amortization. The pension manager invests in the financial market with three assets: cash, bond and stock. Regardless of the initial status of the plan, we suppose that the pension fund may become underfunded or overfunded in the planning horizon. The optimization goal of the manager is to maximize the expected utility in the overfunded region minus the weighted solvency risk in the underfunded region. By introducing an auxiliary process and related equivalent optimization problems and using the martingale method, the optimal wealth process, optimal portfolio and efficient frontier are obtained under four cases (high tolerance towards solvency risk, low tolerance towards solvency risk, a specific lower bound, and high lower bound). Moreover, we also obtain the probabilities that the optimal terminal wealth falls in the overfunded and underfunded regions. At last, we present numerical analyses to illustrate the manager's economic behaviors. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.08731&r=upt |
| By: | Eduardo Dávila; Andreas Schaab |
| Abstract: | This paper characterizes optimal monetary policy in a canonical heterogeneous-agent New Keynesian (HANK) model with wage rigidity. Under discretion, a utilitarian planner faces the incentive to redistribute towards indebted, high marginal utility households, which is a new source of inflationary bias. With commitment, i) zero inflation is the optimal long-run policy, ii) time-consistent policy requires both inflation and distributional penalties, and iii) the planner trades off aggregate stabilization against distributional considerations, so Divine Coincidence fails. We compute optimal stabilization policy in response to productivity, demand, and cost-push shocks using sequence-space methods, which we extend to Ramsey problems and welfare analysis. |
| JEL: | E52 E61 |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30961&r=upt |
| By: | Marion Collewet (Universiteit Leiden); Paul Koster (Vrije Universiteit Amsterdam) |
| Abstract: | Point allocation experiments are widely used in the social sciences. In these experiments, survey respondents distribute a fixed total number of points across a fixed number of alternatives. This paper reviews the different perspectives in the literature about what respondents do when they distribute points across options. We find three main alternative interpretations in the literature, each having different implications for empirical work. We connect these interpretations to models of utility maximization that account for point and budget constraints and investigate the role of budget constraints in more detail. We show how these constraints impact the regression specifications for point allocation experiments that are commonly used in the literature. We also show how a formulation of a taste for variety as entropy that had been previously used to analyse market shares can fruitfully be applied to choice behaviour in point allocation experiments. |
| Keywords: | constant-sum paired comparison, probabilistic choice, entropy, constrained optimization |
| Date: | 2023–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230012&r=upt |
| By: | Lorena Torres Lahoz (DTU Management, Technical University of Denmark); Francisco Camara Pereira (DTU Management, Technical University of Denmark); Georges Sfeir (DTU Management, Technical University of Denmark); Ioanna Arkoudi (DTU Management, Technical University of Denmark); Mayara Moraes Monteiro (DTU Management, Technical University of Denmark); Carlos Lima Azevedo (DTU Management, Technical University of Denmark) |
| Abstract: | Latent Class Choice Models (LCCM) are extensions of discrete choice models (DCMs) that capture unobserved heterogeneity in the choice process by segmenting the population based on the assumption of preference similarities. We present a method of efficiently incorporating attitudinal indicators in the specification of LCCM, by introducing Artificial Neural Networks (ANN) to formulate latent variables constructs. This formulation overcomes structural equations in its capability of exploring the relationship between the attitudinal indicators and the decision choice, given the Machine Learning (ML) flexibility and power in capturing unobserved and complex behavioural features, such as attitudes and beliefs. All of this while still maintaining the consistency of the theoretical assumptions presented in the Generalized Random Utility model and the interpretability of the estimated parameters. We test our proposed framework for estimating a Car-Sharing (CS) service subscription choice with stated preference data from Copenhagen, Denmark. The results show that our proposed approach provides a complete and realistic segmentation, which helps design better policies. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.09871&r=upt |
| By: | Yoshio Kamijo (Waseda University) |
| Abstract: | Negotiation is at the hear of communication, social exchange, and economic transactions. Using the bargaing model as the unit of analysis, this study aims to deepen our under-standing of negotiation and economic behavior based on the behavioral bargaining theory (BBT) developed by Kamijo and Yokote (2022). We introduce a key concept to analyze a bargaining situation: the stability of entitlements (people's expectations of distribution or sense of ownership) for a bargaining pie. When a pair of entitlements initially formed is stable, negotiations are expected to end immediately; when unstable, negotiations are more likely to end in delay or failure. We show the boundary condition for stable entitlements and find that some unequal distribution between two players can be stable even for a symmetric bargaining problem. By seeking stable entitlements for all members of society, it is possible to define a distribution norm mathematically. We show that the distribution norm that arises in a symmetric situation is the golden rule of distribution: 50–50 split of the pie. Finally, by examining the dynamic process of the formation of entitlements, we clarify the sufficient conditions under which the equal split norm emerges. |
| Keywords: | Behavioral bargaining theory, Nash solution, Reference dependent utility, Stable entitlement, Inequality cap theorem, Distribution norm, Equal split norm |
| Date: | 2023–01 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2209&r=upt |
| By: | Lijun Bo; Yijie Huang; Xiang Yu |
| Abstract: | This paper studies a nonstandard stochastic control problem motivated by the optimal consumption in an incomplete market with wealth tracking of a non-decreasing benchmark process. In particular, the monotone benchmark is modelled by the running maximum of a drifted Brownian motion. We consider a relaxed tracking formulation using capital injection such that the wealth compensated by the injected capital dominates the benchmark process at all times. The stochastic control problem is to maximize the expected utility on consumption deducted by the cost of the capital injection under the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problem is formulated and studied such that the singular control of capital injection and the floor constraint can be hidden. To tackle the HJB equation with two Neumann boundary conditions, we establish the existence of a unique classical solution to the dual PDE in a separation form using some novel probabilistic representations involving the dual reflected processes and the local time. The proof of the verification theorem on the optimal feedback control can be carried out by some technical stochastic flow analysis of the dual reflected processes and estimations of the optimal control. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.08302&r=upt |
| By: | Michele Bernasconi (Department of Economics, University Of Venice CÃ Foscari); Enrico Longo (University of Hamburg); Valeria Maggian (Department of Economics, University Of Venice CÃ Foscari) |
| Abstract: | We experimentally investigate subjects’ preferences for redistribution depending on i) their personal stake in the outcome (either absent or not), ii) the effect of luck in strengthening or weakening the income inequality as derived from merit, and iii) whether individuals are informed about their relative wealth position in the society or not. We find that self-interest is the main driver of subjects’ redistributive choices when they have direct monetary interests in the outcome. Leaving subjects under the veil of ignorance about their relative gross income position reduces selfish behavior, also controlling for beliefs and risk attitude. Inequality aversion and fairness mostly affect redistributive choices of impartial spectators when recipients of redistribution are not informed about their initial endowments, suggesting that the luck vs. merit effect is not the only driver of redistribution on behalf of others. |
| Keywords: | Income redistribution, Inequality aversion, Fairness, Experiment |
| JEL: | D31 D63 D81 C91 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2023:02&r=upt |
| By: | Attanasi, Giuseppe (University of Nice Sophia-Antipolis); Rimbaud, Claire (University of Lyon 2); Villeval, Marie Claire (CNRS, GATE) |
| Abstract: | We investigate whether a player's guilt aversion is modulated by the co-players' vulnerability. To this goal, we introduce new variations of a three-player Trust game in which we manipulate payoff vulnerability and endowment vulnerability. The former is the traditional vulnerability which arises when a player's material payoff depends on another player's action (e.g., recipient's payoff in a Dictator game). The latter arises when a player's initial endowment is entrusted to another player (e.g., trustor's endowment in a Trust game). Treatments vary whether trustees can condition their decision on the belief of a co-player who is payoff-vulnerable and/or endowment-vulnerable, or not vulnerable at all, and the decision rights of the vulnerable player. We find that trustees' guilt aversion is insensitive to the dimension of the co-player's vulnerability and to the decision rights of the co-player. Guilt is activated even absent vulnerability of the co-player whose beliefs are disappointed. It is triggered by the willingness to respond to the co-player's beliefs on his strategy, regardless of whether this strategy concerns this player or a third player's vulnerability, that is, indirect vulnerability. |
| Keywords: | guilt aversion, vulnerability, psychological game theory, Dictator game, Trust game, experiment |
| JEL: | C72 C91 D91 |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15960&r=upt |
| By: | Shuoqing Deng; Xiang Yu; Jiacheng Zhang |
| Abstract: | This paper studies the central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with a smooth aggregation preference to incorporate all heterogeneous discount rates with an attitude function that reflects the aggregation rule in the same spirit of ambiguity aversion in the smooth ambiguity preference proposed in Klibanoff et al.(2005). The optimal stopping problem renders to be time inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent equilibria as fixed points of an operator in the setting of one-dimensional diffusion processes. We provide some sufficient conditions on both the underlying models and the attitude function such that the smallest equilibrium attains the optimal equilibrium in which the attitude function becomes equivalent to the linear aggregation rule as of diversity neutral. When the sufficient condition of the attitude function is violated, we can illustrate by various examples that the characterization of the optimal equilibrium may differ significantly from some existing results for an individual agent, which now sensitively depends on the attitude function and the diversity distribution of discount rates. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.07470&r=upt |
| By: | Lin He; Zongxia Liang; Zhaojie Ren; Yilun Song |
| Abstract: | In order to deal with the aging problem, pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the ``Samuelson-Aaron" criterion to age-dependent preference orderings. And we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort's population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts' weight in the government decision-making. The optimal mix is the comprehensive result of the two effects. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.09218&r=upt |
| By: | Xiang Gao; Kees Koedijk; Thomas Walther; Zhan Wang |
| Abstract: | This paper proposes a new metric to gauge investor sentiment using a relative valuation method. We combine investor behavioral finance traits and option-implied standard deviations under both the real-world probability (P) valued most in the view of uninformed investors and the risk-neutral space (Q) adopted when there exists no cognitive error. Given that investor sentiment can be thought of as risk-taking by the uninformed exceeding their informed peers, we postulate that the differences between the variance, skewness, and kurtosis of P and Q measures for investors with various behavioral traits matter. We hence construct our investor sentiment proxy by summing these differentials of variance, skewness, and kurtosis in weighted forms. It is documented that such relative investor sentiment metric exhibits economically and statistically strong return predictability for momentum portfolios. Our findings contribute to the extant literature by (1) complementing the Baker-Wurgler market-based investor sentiment index from the theoretical perspective, (2) modeling investor sentiment via utilizing the informational content of options prices, and (3) supporting the Barberis-Shleifer-Vishny definition of investor sentiment to be differences in financial market participant behavior. |
| Keywords: | sentiment, emotional bias, cognitive error, bounded rationality, preservers, accumulators, momentum, return predictability |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:use:tkiwps:2205&r=upt |
| By: | J.X. Cruz Neto (UFPI - Universidade Federal do Piauí); J. O. Lopes (UFPI - Universidade Federal do Piauí); Antoine Soubeyran (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); João Carlos O. Souza (UFPI - Universidade Federal do Piauí) |
| Abstract: | In this paper, we consider an abstract regularized method with a skew-symmetric mapping as regularization for solving equilibrium problems. The regularized equilibrium problem can be viewed as a generalized mixed equilibrium problem and some existence and uniqueness results are analyzed in order to study the convergence properties of the algorithm. The proposed method retrieves some existing one in the literature on equilibrium problems. We provide some numerical tests to illustrate the performance of the method. We also propose an original application to Becker's household behavior theory using the variational rationality approach of human dynamics. |
| Keywords: | Equilibrium problem, Variational rationality, Desires, Traps, Household behavior, Resource allocation problems |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03544673&r=upt |
| By: | Yuhong Xu; Shih-Fen Cheng; Xinyu Chen |
| Abstract: | In domains where agents interact strategically, game theory is applied widely to predict how agents would behave. However, game-theoretic predictions are based on the assumption that agents are fully rational and believe in equilibrium plays, which unfortunately are mostly not true when human decision makers are involved. To address this limitation, a number of behavioral game-theoretic models are defined to account for the limited rationality of human decision makers. The "quantal cognitive hierarchy" (QCH) model, which is one of the more recent models, is demonstrated to be the state-of-art model for predicting human behaviors in normal-form games. The QCH model assumes that agents in games can be both non-strategic (level-0) and strategic (level-$k$). For level-0 agents, they choose their strategies irrespective of other agents. For level-$k$ agents, they assume that other agents would be behaving at levels less than $k$ and best respond against them. However, an important assumption of the QCH model is that the distribution of agents' levels follows a Poisson distribution. In this paper, we relax this assumption and design a learning-based method at the population level to iteratively estimate the empirical distribution of agents' reasoning levels. By using a real-world dataset from the Swedish lowest unique positive integer game, we demonstrate how our refined QCH model and the iterative solution-seeking process can be used in providing a more accurate behavioral model for agents. This leads to better performance in fitting the real data and allows us to track an agent's progress in learning to play strategically over multiple rounds. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.06033&r=upt |