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on Utility Models and Prospect Theory |
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Issue of 2022‒08‒22
thirteen papers chosen by |
| By: | J. Cerda-Hernandez; A. Sikov |
| Abstract: | In this work, we examine the combined problem of optimal portfolio selection rules for an insurer in a continuous time model where the surplus of an insurance company is modelled as a compound Poisson process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. According to utility theory, in a financial market where investors are facing uncertainty, an investor is not concerned with wealth maximization per se but with utility maximization. It is therefore possible to introduce an increasing and concave utility function $\phi(x,t)$ representing the expected utility of a risk averse investor (insurance company). Therefore, the goal of this work is not anymore to maximize the expected portfolio value or minimize the ruin probability or maximizing the expectation of the present value of all dividends paid to the shareholders up to the ruin, but to maximize the expected utility stemming from the wealth during the life contract [0,T]. In this direction, using the Dynamic Programming Principle of the problem, we obtain the Hamilton-Jacobi-Bellman equation by our optimization problem (HJB). Finally, we present numerical solutions in some cases, obtaining as optimal strategy the well known Merton's strategy. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.02947&r= |
| By: | Gabriel Montes-Rojas (Instituto Interdisciplinario de Economía Política de Buenos Aires - UBA - CONICET); Luciano de Castro (University of Iowa); Antonio F. Galvao (Michigan State University); Jeong Yeol Kim (University of Arizona); José Olmo (Universidad de Zaragoza; University of Southampton) |
| Abstract: | This paper conducts a laboratory experiment to assess the optimal allocation under quantile preferences (QP) and compares the model predictions with those of a meanvariance (MV) utility function. We estimate the aversion coefficients associated to the individuals’ empirical portfolio under the QP and MV theories, and evaluate the relative predictive of each theory. The experiment assesses individuals’ preferences through a portfolio choice experiment constructed from two assets that may include a risk-free asset. The results of the experiment con rm the suitability of both to predict individuals’ optimal choices. Furthermore, the aggregation of results by individual choices o ers support to the MV theory. However, the aggregation of results by task, which is more informative, provides more support to the QP theory. The overall message that emerges from this experiment is that individuals’ behavior is better predicted by the MV model when it is di cult to assess the differences in the lotteries’ payoff distributions but better described as QP maximizers, otherwise. |
| Keywords: | Optimal asset allocation, Quantile preferences, Portfolio theory, Risk attitude, Predictive ability test |
| JEL: | D81 G11 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:ake:iiepdt:202168&r= |
| By: | Rutledge, Robert (University of Sydney); Alladi, Vinayak (University of Sydney); Cheung, Stephen L. (University of Sydney) |
| Abstract: | We experimentally test Kőszegi and Rabin's (2006, 2007) theory of reference-dependent preferences in the context of price expectations. In an incentivised valuation task, participants are endowed with a mug and provide their willingness to accept (WTA) to sell it. We manipulate the sale price in a separate, exogenous forced sale scenario, which is predicted to produce a 'comparison effect', moving WTA in the opposite direction to the forced sale price. Consistent with the theory, we observe a treatment effect of between AUD $0.79 and $2.06 in the hypothesised direction; however, it is statistically insignificant. We also elicit participants' loss aversion to account for heterogeneity in the theorised effect; however, controlling for the interaction between our treatment and loss aversion does not consistently strengthen our result. |
| Keywords: | reference dependence, price expectations, comparison effect, loss aversion |
| JEL: | C91 D90 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15375&r= |
| By: | Anay Mehrota (Yale University); Bary S. R. Pradelski (CNRS); Nisheeth K. Vishnoi (Cowles Foundation, Yale University) |
| Abstract: | In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation produces persistent inequality and reduces utility for the decision-maker. Recent works show that interventions like the Rooney Rule, which require a minimum quota of individuals from each affected group, are very effective in improving utility when individuals belong to at most one affected group. However, in several settings, individuals belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, with intersectionality, the aforementioned non-intersectional constraints only recover part of the utility achievable in the absence of implicit bias. On the other hand, we show that appropriate lower-bound constraints on the intersections recover almost all the utility achievable in the absence of implicit bias. And, hence, offer an advantage over non-intersectional approaches to reducing inequality. |
| Keywords: | Implicit bias, selection, Hiring, Screening, Intersectionality, Intersectional biases, Affirmative Action, Rooney Rule, Antidiscrimination Policy, Social Factors on Decision Making |
| JEL: | J71 J78 D91 D63 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2335&r= |
| By: | Charl Maree; Christian W. Omlin |
| Abstract: | Stock portfolio optimization is the process of continuous reallocation of funds to a selection of stocks. This is a particularly well-suited problem for reinforcement learning, as daily rewards are compounding and objective functions may include more than just profit, e.g., risk and sustainability. We developed a novel utility function with the Sharpe ratio representing risk and the environmental, social, and governance score (ESG) representing sustainability. We show that a state-of-the-art policy gradient method - multi-agent deep deterministic policy gradients (MADDPG) - fails to find the optimum policy due to flat policy gradients and we therefore replaced gradient descent with a genetic algorithm for parameter optimization. We show that our system outperforms MADDPG while improving on deep Q-learning approaches by allowing for continuous action spaces. Crucially, by incorporating risk and sustainability criteria in the utility function, we improve on the state-of-the-art in reinforcement learning for portfolio optimization; risk and sustainability are essential in any modern trading strategy and we propose a system that does not merely report these metrics, but that actively optimizes the portfolio to improve on them. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.02134&r= |
| By: | Xiaoshan Chen; Xun Li; Fahuai Yi; Xiang Yu |
| Abstract: | This paper studies a finite horizon utility maximization problem on excessive consumption under a drawdown constraint up to the bankruptcy time. Our control problem is an extension of the one considered in Bahman et al. (2019) to the model with a finite horizon and also an extension of the one considered in Jeon and Oh (2022) to the model with zero interest rate. Contrary to Bahman et al. (2019), we encounter a parabolic nonlinear HJB variational inequality with a gradient constraint, in which some time-dependent free boundaries complicate the analysis significantly. Meanwhile, our methodology is built on technical PDE arguments, which differs substantially from the martingale approach in Jeon and Oh (2022). Using dual transform and considering some auxiliary parabolic variational inequalities with both gradient and function constraints, we establish the existence and uniqueness of the classical solution to the HJB variational inequality and characterize all associated free boundaries in analytical form. Consequently, the piecewise optimal feedback controls and some time-dependent thresholds of the wealth variable for different control expressions can be obtained. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.07848&r= |
| By: | Ante Sterc |
| Abstract: | This study characterizes the household’s choice of investment fund as a multiple step procedure. Using two structural econometric models, I estimate potential investor characteristics that drive the decision process. While the first step includes choosing whether to invest in a fund or not, i.e. it models the extensive margin, the second step models the intensive margin, depending on the choice of the econometric model. In the first step, the probability of becoming a fund investor rises with the level of education, financial literacy and wealth, but falls with age and indebtedness. In the second step, the investment size increases with wealth and age but decreases with financial literacy. Further, I model the choice between different types of investment funds as extensions of the Random Utility Model (RUM) - representing full consideration - and the Limited Consideration Model. In this way, I am able to estimate and compare resulting models. I reject full consideration in favor of limited consideration behavior. Using a novel framework for investment fund choice, I estimate average monetary losses affected by limited consideration. In contrast to previous research that uses only the full consideration framework, I find that all households across the wealth distribution face significant losses. However, conditional on wealth, households with a lower level of education or financial literacy face larger losses. In addition, by combining results from multiple steps of the investment decision, I calculate the elasticity of marginal utility of investing in variables such as financial literacy. |
| Keywords: | investment fund choice; limited consideration; financial literacy; |
| JEL: | D83 G11 G23 G41 G53 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp729&r= |
| By: | Caroline Hillairet; Sarah Kaakai; Mohamed Mrad |
| Abstract: | This paper proposes and investigates an optimal pair investment/pension policy for a pay-as-you-go (PAYG) pension scheme. The social planner can invest in a buffer fund in order to guarantee a minimal pension amount. The model aims at taking into account complex dynamic phenomena such as the demographic risk and its evolution over time, the time and age dependence of agents preferences, and financial risks. The preference criterion of the social planner is modeled by a consistent dynamic utility defined on a stochastic domain, which incorporates the heterogeneity of overlapping generations and its evolution over time. The preference criterion and the optimization problem also incorporate sustainability, adequacy and fairness constraints. The paper designs and solves the social planner's dynamic decision criterion, and computes the optimal investment/pension policy in a general framework. A detailed analysis for the case of dynamic power utilities is provided. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.01536&r= |
| By: | Kim Weston |
| Abstract: | A limited participation economy models the real-world phenomenon that some economic agents have access to more of the financial market than others. We prove the global existence of a Radner equilibrium with limited participation, where the agents have exponential preferences and derive utility from both running consumption and terminal wealth. Our analysis centers around the existence and uniqueness of a solution to a coupled system of quadratic backward stochastic differential equations (BSDEs). We prove that the BSDE system has a unique $\mathcal{S}^\infty\times\text{bmo}$ solution. We define a candidate equilibrium in terms of the BSDE solution and prove through a verification argument that the candidate is a Radner equilibrium with limited participation. This work generalizes the model of Basak and Cuoco (1998) to allow for a stock with a general dividend stream and agents with exponential preferences. We also provide an explicit example. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.12399&r= |
| By: | Khanal, Aditya R.; Mishra, Ashok K.; Lien, Gudbrand |
| Keywords: | Risk and Uncertainty, Production Economics, International Development |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaea22:322239&r= |
| By: | Mughal, Adil Ahmad |
| Abstract: | Transcendental Analytic, in Critique of Pure Reason, combines the space and time as conditions of the possibility of phenomenon from Transcendental Aesthetic with the pure magnitude-intuition notion. The property of continuity as a qualitative result of the additive magnitude brings the possibility of connecting with experience, even though only as a potential because of the a priori necessity from assumption, as syntheticity of the a priori task of a scientific method of philosophy given by Kant, which precludes the application of categories to something not empirically reducible to the content of such a category's corresponding and possible object. This continuity as the qualitative result of a priori constructed notion of magnitude lies as a fundamental assumption and property of, what in Microeconomic theory is called as, 'choice rules' which combine the potentially-empirical and practical budget-price pairs with preference relations. This latter result is the purest qualitative side of the choice rules' otherwise autonomously quantitative nature. The theoretical, barring the empirical, nature of this qualitative result is a synthetic a priori truth, which, if at all, it should be, if the axiomatic structure of economic theory is held to be correct. It has a potentially verifiable content as its possible object in the form of quantitative price-budget pairs, yet, the object that serves the respective Kantian category is qualitative itself which is utility. This article explores the validity of Kantian qualifications for this application of 'categories' to the economic structure of society. |
| Keywords: | Categories of Understanding, Continuity, Convexity, Psyche, Revealed Preferences, Synthetic a priori |
| JEL: | B4 B49 D0 D01 D9 |
| Date: | 2022–06–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:113677&r= |
| By: | Huaxin Wang-Lu; Octasiano Miguel Valerio Mendoza |
| Abstract: | China's structural changes have brought new challenges to its regional employment structure, entailing spatial redistribution of workforce. However, Chinese research on migration decisions involving future outcomes and on city-level bilateral longitudinal determinants is almost non-existent. This paper sheds light on the effects of sector-based job prospects on individual migration decisions across prefecture boundaries. To this end, we created a proxy variable for job prospects, compiled a unique quasi-panel of 66,427 individuals from 283 cities during 1997--2017, expanded the random utility maximisation model of migration by introducing the reference-dependence, derived empirical specifications with theoretical micro-foundations and applied various monadic and dyadic fixed effects to address multilateral resistance to migration. Multilevel logit models and two-step system GMM estimation were adopted for the robustness check. Our primary findings are that a 10% increase in the ratio of sector-based job prospects in cities of destination to cities of origin raises the probability of migration by 1.281--2.185 percentage points, and the effects tend to be stronger when the scale of the ratio is larger. Having a family migration network causes an increase of approximately 6 percentage points in migratory probabilities. Further, labour migrants are more likely to be male, unmarried, younger, or more educated. Our results suggest that the ongoing industrial reform in China influences labour mobility between prefecture-level cities, providing important insights for regional policymakers to prevent brain drain and to attract relevant talent. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.08282&r= |
| By: | Jamie Tucker-Foltz; Richard Zeckhauser |
| Abstract: | We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive private values for the goods. The prior distributions on those values are independent and common knowledge. We characterize the structure of optimal divisions in the divide-and-choose game and show how to efficiently compute equilibria. We identify several striking differences between optimal strategies in the cases of known versus unknown preferences. Most notably, the divider has a compelling "diversification" incentive in creating the chooser's two options. This incentive, hereto unnoticed, leads to multiple goods being divided at equilibrium, quite contrary to the divider's optimal strategy when preferences are known. In many contexts, such as buy-and-sell provisions between partners, or in judging fairness, it is important to assess the relative expected utilities of the divider and chooser. Those utilities, we show, depend on the players' uncertainties about each other's values, the number of goods being divided, and whether the divider can offer multiple alternative divisions. We prove that, when values are independently and identically distributed across players and goods, the chooser is strictly better off for a small number of goods, while the divider is strictly better off for a large number of goods. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.03076&r= |