
on Utility Models and Prospect Theory 
By:  Misha Perepelitsa 
Abstract:  A family of models of individual discrete choice are constructed by means of statistical averaging of choices made by a subject in a reinforcement learning process, where the subject has short, kterm memory span. The choice probabilities in these models combine in a nontrivial, nonlinear way the initial learning bias and the experience gained through learning. The properties of such models are discussed and, in particular, it is shown that probabilities deviate from Luce's Choice Axiom, even if the initial bias adheres to it. Moreover, we shown that the latter property is recovered as the memory span becomes large. Two applications in utility theory are considered. In the first, we use the discrete choice model to generate binary preference relation on simple lotteries. We show that the preferences violate transitivity and independence axioms of expected utility theory. Furthermore, we establish the dependence of the preferences on frames, with risk aversion for gains, and risk seeking for losses. Based on these findings we propose next a parametric model of choice based on the probability maximization principle, as a model for deviations from expected utility principle. To illustrate the approach we apply it to the classical problem of demand for insurance. 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.06133&r=all 
By:  Christoph Kuzmics (University of Graz, Austria); Brian W. Rogers (Washington University in St. Louis, USA); Xiannong Zhang (Washington University in St. Louis, USA) 
Abstract:  We perform two types of lab experiments to assess the normative and positive appeal of preference models exhibiting ambiguity aversion. Our first experiment is a simple extension of the Ellsberg [1961] twocolor urn experiment in which there is an option that hedges ambiguity away completely and that dominates the options that correspond to Ellsberg behavior. 63% of subjects choose the dominated Ellsberg options, which compares similarly to the proportion of subjects choosing the risky urn in the standard twocolor experiment. While subjective expected utility cannot explain this choice, also none of the classical models of ambiguity aversion can explain this choice. Our second experiment is also based on the Ellsberg twocolor urn experiment. In this experiment, in various treatments, we provide advice in the form of short video clips in favor of, as well as against, the Ellsberg choice. We find suggestive, but not conclusive, evidence that subjects' choices are influenced by advice and, in these cases, mostly in the direction of abandoning the Ellsberg option. 
Keywords:  Knightian uncertainty; Subjective expected utility; Ambiguity aversion; lab experiment 
JEL:  C91 D81 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:grz:wpaper:201907&r=all 
By:  Fabrizio Adriani (University of Leicester); Silvia Sonderegger (University of Nottingham) 
Abstract:  We use a simple costbenefit analysis to derive optimal similarity judgments  addressing the question: when should we expect a decision maker to distinguish between different time periods or different prizes? Our key premise is that cognitive resources are costly and are to be deployed only where they really matter. We show that this simple insight can explain a number of observed anomalies, such as: (i) time preference reversal, (ii) magnitude effects, (iii) interval length effects. For each of these phenomena, our approach allows to identify the direction of the bias relative to the benchmark case where cognitive resources are costless. Finally, we show that, when applied to choice under risk, the same insights predict anomalies such as the ratio and certainty effects, and rationalize Rabin's risk aversion paradox. This suggests that the theory may provide a parsimonious explanation of behavioral anomalies in different contexts. 
Keywords:  Similarity judgments, Intertemporal Choice, Rational Inattention, Choice Under Risk 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201906&r=all 
By:  Ankush Agarwal; Matthew Lorig 
Abstract:  In an incomplete market, including liquidlytraded European options in an investment portfolio could potentially improve the expected terminal utility for a riskaverse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept  the implied Sharpe ratio  which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor's portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the statedependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's riskaversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio. 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.04837&r=all 
By:  Subhojit Biswas; Diganta Mukherjee 
Abstract:  We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices return. We use Markov Decision Process and dynamic programming principle to get the optimal strategies and the value function which maximize the expected utility for parametric as well as non parametric distributions. Due to lack of explicit solution in the non parametric case, we use numerical integration for optimization 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.03907&r=all 
By:  Martin, Ian; Papadimitriou, Dimitris 
Abstract:  We present a dynamic model featuring riskaverse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so "the market" is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. 
Keywords:  Excess Volatility; heterogeneous beliefs; sentiment; Speculation; target prices 
JEL:  E44 G02 G11 G12 G13 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:13857&r=all 
By:  Subhojit Biswas; Mrinal K. Ghosh; Diganta Mukherjee 
Abstract:  We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of the stock prices return. We use a stochastic maximum principle to formulate the dynamic optimisation problem. The equations which we obtain does not have any explicit analytical solution, so we look for accurate approximations to estimate the value function and optimal strategy. As our calibration strategy is nonparametric in nature, no prior knowledge on the form of the distribution function is needed. We also provide detailed empirical illustration using real life data. Our results show close concordance with financial intuition.We expect that our results will add to the arsenal of the high frequency traders. 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.03905&r=all 
By:  Matthew Gould; Matthew D. Rablen 
Abstract:  We focus on the preferences of an extremely salient group of highlyexperienced individuals who are entrusted with making decisions that affect the lives of millions of their citizens, heads of government. We test for the presence of a fundamental behavioral bias, loss aversion, in the way heads of government choose decision rules for international organizations. If loss aversion disappears with experience and highstakes it should not exhibited in this context. Loss averse leaders choose decision rules that oversupply negative (blocking) power at the expense of positive power (to initiate affirmative action), causing welfare losses through harmful policy persistence and reform deadlocks. We find evidence of significant loss aversion (λ = 4:4) in the Qualified Majority rule in the Treaty of Lisbon, when understood as a Nash bargaining outcome. World leaders may be more loss averse than the populous they represent. 
Keywords:  loss aversion, behavioral biases, constitutional design, voting, bargaining, voting power, EU Council of Ministers 
JEL:  D03 D81 D72 C78 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_7763&r=all 
By:  Hans Carlsson; Philipp Christoph Wichardt 
Abstract:  This paper proposes a comprehensive perspective on the question of selfenforcing solutions for normal form games. While this question has been widely discussed in the literature, the focus is usually either on strict incentives for players to stay within the proposed solution or on strategic uncertainty, i.e. robustness to trembles. The present approach combines both requirements in proposing the concept of robust sets, i.e. sets of strategy profiles which satisfy both strict incentives and robustness to strategic uncertainty. The result is a set valued solution, a variant of which is shown to exist for all finite normal form games. 
Keywords:  game theory, selfenforcing solution, strict incentives, strategic uncertainty 
JEL:  C72 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_7715&r=all 
By:  Jos\'e Cl\'audio do Nascimento 
Abstract:  A theory usually comprises assumptions and deduced predictions from them. In this paper, empirical evidences corroborate with assumptions about time for a decision making facing known probabilities and outcomes. 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.01709&r=all 
By:  Sanjit Dhami; Junaid Arshad; Ali alNowaihi 
Abstract:  Microfinance contracts have enormous economic and welfare significance. We study, theoretically and empirically, the problem of effort choice under individual liability (IL) and joint liability (JL) contracts when loan repayments are made either privately, or publicly in front of one’s social group. Our theoretical model identifies guilt from letting down the expectations of partners in a JL contract, and shame from falling short of normatively inadequate effort, under public repayment of loans, as the main psychological drivers of effort choice. Evidence from our labinthefield experiment in Pakistan reveals large treatment effects and confirms the central roles of guilt and shame. Under private repayment, a JL contract increases effort by almost 100% relative to an IL contract. Under public repayment, effort levels are comparable under IL and JL contracts, which is consistent with recent empirical results. This indicates that shameaversion plays a more important role as compared to guiltaversion. Under IL, repayment in public relative to private repayment increases effort by 60%, confirming our shameaversion hypothesis. Under JL, a comparison of private and public repayment shows that shame trumps guilt in explaining effort choices of borrowers. 
Keywords:  microfinance, joint/individual liability, public/private repayment, beliefdependent motivations, guilt, shame, peer pressure, social capital, labinthefield experiment 
JEL:  C91 C92 D82 D91 G21 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_7773&r=all 
By:  Mariana Carrera; Heather Royer; Mark Stehr; Justin Sydnor; Dmitry Taubinsky 
Abstract:  A large literature treats takeup of commitment contracts, in the form of choiceset restrictions or penalties, as a smoking gun for (awareness of) selfcontrol problems. This paper provides new techniques for examining the validity of this assumption, as well as a new approach for detecting (awareness of) selfcontrol problems. Theoretically, we show that with some uncertainty about the future, demand for commitment contracts is closer to a special case than to a robust implication of models of limited selfcontrol. In a field experiment with 1292 members of a fitness facility, we find that many participants take up commitment contracts both for going to the gym more and for going to the gym less, and there is a significant positive correlation in demand for these two types of contracts. This suggests that commitment contract takeup reflects, at least in part, something other than the desire to change own future behavior, such as demand effects or "noisy valuation." Moreover, we find that commitment contract takeup is negatively related to awareness of selfcontrol problems: a novel information treatment that increased awareness of selfcontrol problems reduced demand for commitment contracts. We address the limitations of using commitment contracts as a measurement tool by showing that a combination of belief forecasts and willingness to pay for linear incentives provides more robust identification of limited selfcontrol and people's awareness of it. We use the methodology to obtain some of the first parameter estimates of partiallysophisticated quasihyperbolic discounting in the field. 
JEL:  C9 D9 I12 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:26161&r=all 
By:  Fedor Sandomirskiy; Erel SegalHalevi 
Abstract:  A set of objects, some goods and some bads, is to be divided fairly among agents with different tastes, modeled by additive utilityfunctions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then fair division may not exist. What is the smallest number of objects that must be shared between two or more agents in order to attain a fair division? We focus on Paretooptimal, envyfree and/or proportional allocations. We show that, for a generic instance of the problem  all instances except of a zeromeasure set of degenerate problems  a fair and Paretooptimal division with the smallest possible number of shared objects can be found in polynomial time, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where the agents' valuations are aligned for many objects. 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.01669&r=all 
By:  Jonathan Benchimol (Bank of Israel); Lahcen Bounader (International Monetary Fund, Washington, D.C., United States) 
Abstract:  Abstract We build a behavioral New Keynesian model that emphasizes different forms of myopia for households and firms. By examining the optimal monetary policy within this model, we find four main results. First, in a framework where myopia distorts agents' inflation expectations, the optimal monetary policy entails implementing inflation targeting. Second, price level targeting emerges as the optimal policy under output gap, revenue, or interest rate myopia. Given that bygones are not bygones under price level targeting, rational inflation expectations are a minimal condition for optimality in a behavioral world. Third, we show that there are no feasible instrument rules for implementing the optimal monetary policy, casting doubt on the ability of simple Taylor rules to assist in the setting of monetary policy. Fourth, bounded rationality may be associated with welfare gains. 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:boi:wpaper:2019.07&r=all 
By:  Farhad Farokhi 
Abstract:  In this paper, we define discounted differential privacy, as an alternative to (conventional) differential privacy, to investigate privacy of evolving datasets, containing time series over an unbounded horizon. Evolving datasets arise in energy systems (e.g., realtime smart meter measurements), transportation (e.g., realtime traces of individual movements), and retail industry (e.g., customer interactions and purchases from online stores). We first define privacy loss as a measure of the amount of information leaked by the reports at a certain fixed time and relate privacy loss to differential privacy. We observe that privacy losses are weighted equally across time in the definition of differential privacy, and therefore the magnitude of privacypreserving additive noise must grow without bound to ensure differential privacy over an infinite horizon. Motivated by the discounted utility theory within the economics literature, we use exponential and hyperbolic discounting of privacy losses across time to relax the definition of differential privacy under continual observations. This implies that privacy losses in a distant past are less important than the current ones to an individual. We use discounted differential privacy to investigate privacy of evolving datasets using additive Laplace noise and show that the magnitude of the additive noise can remain bounded under discounted differential privacy. We illustrate the quality of privacypreserving mechanisms satisfying discounted differential privacy on smartmeter measurement timeseries of real households, made publicly available by the Ausgrid (an Australian electricity distribution company). 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.03995&r=all 