
on Utility Models and Prospect Theory 
By:  Kristof Wiedermann 
Abstract:  We consider the utility maximization problem under convex constraints with regard to theoretical results which allow the formulation of algorithmic solvers which make use of deep learning techniques. In particular for the case of random coefficients, we prove a stochastic maximum principle (SMP), which also holds for utility functions $U$ with $\mathrm{id}_{\mathbb{R}^{+}} \cdot U'$ being not necessarily nonincreasing, like the power utility functions, thereby generalizing the SMP proved by Li and Zheng (2018). We use this SMP together with the strong duality property for defining a new algorithm, which we call deep primal SMP algorithm. Numerical examples illustrate the effectiveness of the proposed algorithm  in particular for higherdimensional problems and problems with random coefficients, which are either path dependent or satisfy their own SDEs. Moreover, our numerical experiments for constrained problems show that the novel deep primal SMP algorithm overcomes the deep SMP algorithm's (see Davey and Zheng (2021)) weakness of erroneously producing the value of the corresponding unconstrained problem. Furthermore, in contrast to the deep controlled 2BSDE algorithm from Davey and Zheng (2021), this algorithm is also applicable to problems with path dependent coefficients. As the deep primal SMP algorithm even yields the most accurate results in many of our studied problems, we can highly recommend its usage. Moreover, we propose a learning procedure based on epochs which improved the results of our algorithm even further. Implementing a semirecurrent network architecture for the control process turned out to be also a valuable advancement. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.07771&r= 
By:  Andrea Antico; Giulio Bottazzi; Daniele Giachini 
Abstract:  The behavioural finance literature attributes the persistent market misvaluation observed in real data to the presence of deviations from rational thinking of the actors involved. Cognitive biases and the use of simple heuristics can be described using expected utility maximising agents that adopt incorrect beliefs. Along these lines, Barberis et al. (1998) introduce a model which is able to replicate the behavior of both underreaction and overreaction to news. The representative agent they consider is characterized by an imperfect learning model. An interesting question that emerges is if, and to what degree, the heuristic mechanism they propose is evolutionary stable, that is how resilient is their representative agent to other agents possibly trading in the market. In fact, if the biased agent asymptotically disappears from the market, the misvaluation patters generated by its behavior does not survive in the long term. The present paper investigates this question comparing the performance of the agent described in Barberis et al. (1998) with the one of a pure Bayesian competitor. 
Keywords:  Learning; Market Selection; Investor Sentiment; Model Misspecification; Financial Markets. 
Date:  2022–03–07 
URL:  http://d.repec.org/n?u=RePEc:ssa:lemwps:2022/09&r= 
By:  Aras, Atilla 
Abstract:  This study provides the solution to the equity premium puzzle. The new model was developed by including the behavior of investors toward risk in financial markets in prior studies. The calculations of this newly tested model show that the value of the coefficient of relative risk aversion is 1.033526 by assuming the value of the subjective time discount factor to be 0.99. Since these values are compatible with the existing empirical studies, they confirm the validity of the newly derived model that provides the solution to the equity premium puzzle. 
Date:  2020–10–31 
URL:  http://d.repec.org/n?u=RePEc:osf:osfxxx:b9afj&r= 
By:  Vincent Laferriere; David Staubli; Christian Thoeni 
Abstract:  We report experimental data from standard market entry games and winnertakeall games. At odds with traditional decision making models with risk aversion, the winnertakeall condition results in substantially more entry than the expectedpayoffequivalent market entry game. We explore three candidate explanations for excess entry: blind spot, illusion of control, and joy of winning, none of which receive empirical support. We provide a novel theoretical explanation for excess entry based on Cumulative Prospect Theory and test it empirically. Our results suggest that excess entry into highly competitive environments is not caused by a genuine preference for competing, but driven by probability weighting. Market entrants overweight the small probabilities associated with the high payoff outcomes in winnertakeall markets, while they underweight probable failures. 
Keywords:  Winnertakeall market, Market entry game, Excess entry, Cumulative Prospect Theory, Probability weighting, Experiment 
JEL:  C92 D81 D91 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:lau:crdeep:22.02&r= 
By:  Luca Henkel (University of Bonn) 
Abstract:  Observed individual behavior in the presence of ambiguity is characterized by insufficient responsiveness to changes in subjective likelihoods. Such likelihood insensitivity under ambiguity is integral to theoretical models and predictive of behavior in many important domains such as financial decisionmaking. However, there is little empirical evidence on its causes and determining factors. This paper investigates the role of beliefs in the form of ambiguity perception  the extent to which a decisionmaker has difficulties assigning a single probability to each possible event  as a potential determinant. Using an experiment, I exogenously vary the degree of ambiguity while eliciting measures of likelihood insensitivity and ambiguity perception. The results provide strong support for an ambiguity perception based explanation of likelihood insensitivity. Not only are the two measures highly correlated on the individual level, but changes in ambiguity perception due to the exogenous variation also directly induce changes in likelihood insensitivity. My evidence thus substantiates the perception based interpretation of likelihood insensitivity brought forward by multiple prior models in contrast to preference based explanations of other commonly used models. 
Keywords:  Ambiguity, decisionmaking under uncertainty, likelihood insensitivity, multiple prior models 
JEL:  D81 D83 D91 C91 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:ajk:ajkdps:151&r= 
By:  Lockwood, Ben (University of Warwick); Le, Minh (University of Warwick); Rockey, James (University of Birmingham) 
Abstract:  This paper explores the implications of voter lossaversion and imperfect recall for the dynamics of electoral competition in a simple Downsian model of repeated elections. We first establish a benchmark result: when the voters’ reference point is forwardlooking, there are a continuum of rational expectations equilibria (REE). When voters are backwardlooking i.e. the reference point is last period’s recalled policy, interesting dynamics only emerge when voters have imperfect recall about that policy. Then, the interplay between the median voter’s reference point and political parties’ choice of platforms generates a dynamic process of polarization (or depolarization). Under the assumption that parties are riskneutral, platforms monotonically converge over time to a longrun equilibrium, which is always a REE. When parties are riskaverse, dynamic incentives also come into play, and generally lead to more policy moderation, resulting in equilibria that are more moderate than the most moderate REE JEL Classification: D72 ; D81 
Keywords:  electoral competition ; repeated elections ; lossaversion ; imperfect recall ; advantage 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:wrk:wqapec:12&r= 
By:  Delphine BOUTIN; Laurène PETIFOUR; Haris MEGZARI 
Abstract:  The salience of the first Covid19 crisis over a wellidentified period represents an unexpected and abrupt change in the environment. This study uses the onset of the Covid19 crisis to empirically examine whether risk and time preferences change in response to this exogenous shock. We use an original panel dataset conducted in January 2020 (before any event) and June 2020 (after the removal of strong economic measures) among women working in the informal sector in Ouagadougou, Burkina Faso. We use individual fixed effects on a balanced panel of 853 women to isolate the specific causal effect of the Covid19 crisis on variation in attitudes toward risk and time over these six months and rule out alternative explanations for differences in preferences. We demonstrate strong preference instability: risk aversion changed over the period in both the gain (13%) and loss (47%) domains, while impatience increased by 9%. We also show that risk aversion (in both domains) is nonsensitive to actual impacts, but appears to be driven by economic fears and concerns related to the Covid19 crisis. We also find that greater exposure to the media reinforces preference instability: the more informed the respondent is, the more their risk and time preferences vary. The same phenomenon is observed when their source of information comes from the government or from a social network (Facebook and WhatsApp). 
Keywords:  Covid19, Risk attitude, Impatience, Emotions, Media exposure 
JEL:  D8 D9 C93 I18 O55 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:grt:bdxewp:202205&r= 
By:  Fay\c{c}al Drissi 
Abstract:  Liquidity issues have been increasingly addressed recently, especially with regards to optimal execution of large orders. In practice, agents facing these issues are uncertain about the future dynamics of the assets, and face the risk of model misspecification, which could make the execution strategies non optimal. In this paper, we address the problem of uncertainty faced by an agent wishing to execute large orders on multiple assets. The agent only has knowledge about the distribution of the future drift of the assets composing her portfolio. We build on the work in [13] who proposed a model coupling Bayesian learning and dynamic programming techniques. More precisely, in this article, we provide a rigorous solution to the problem of portfolio optimal execution where prices have drifted Bachelier dynamics with an unknown drift. The agent uses Bayesian learning to update her estimation of the drift, while she maximizes the expected exponential utility of her final wealth. We consider the specific case where the prior is a nondegenerate multivariate Gaussian, and the costs are quadratic. We use stochastic optimal control tools to show how the problem of optimal execution simplifies into a system of ordinary differential equations (ODEs) which involves a matrix Riccati ODE with timedependent coefficients for which classical existence theorems do not apply. However, using a method similar to the one in [10], we provide a rigorous solution to the problem by using a priori estimates obtained thanks to the original control problem. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.07478&r= 