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on Utility Models and Prospect Theory |
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Issue of 2019‒08‒26
fifteen papers chosen by |
| 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, k-term memory span. The choice probabilities in these models combine in a non-trivial, non-linear 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] two-color 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 two-color 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 two-color 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:2019-07&r=all |
| By: | Fabrizio Adriani (University of Leicester); Silvia Sonderegger (University of Nottingham) |
| Abstract: | We use a simple cost-benefit 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:2019-06&r=all |
| By: | Ankush Agarwal; Matthew Lorig |
| Abstract: | In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse 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 state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's risk-aversion 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 risk-averse 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 non-parametric 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 highly-experienced 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 high-stakes 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 self-enforcing 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, self-enforcing 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 al-Nowaihi |
| 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 lab-in-the-field 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 shame-aversion plays a more important role as compared to guilt-aversion. Under IL, repayment in public relative to private repayment increases effort by 60%, confirming our shame-aversion 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, belief-dependent motivations, guilt, shame, peer pressure, social capital, lab-in-the-field 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 take-up of commitment contracts, in the form of choice-set restrictions or penalties, as a smoking gun for (awareness of) self-control problems. This paper provides new techniques for examining the validity of this assumption, as well as a new approach for detecting (awareness of) self-control 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 self-control. 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 take-up 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 take-up is negatively related to awareness of self-control problems: a novel information treatment that increased awareness of self-control 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 self-control and people's awareness of it. We use the methodology to obtain some of the first parameter estimates of partially-sophisticated quasi-hyperbolic 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 Segal-Halevi |
| Abstract: | A set of objects, some goods and some bads, is to be divided fairly among agents with different tastes, modeled by additive utility-functions. 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 Pareto-optimal, envy-free and/or proportional allocations. We show that, for a generic instance of the problem --- all instances except of a zero-measure set of degenerate problems --- a fair and Pareto-optimal 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., real-time smart meter measurements), transportation (e.g., real-time 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 privacy-preserving 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 privacy-preserving mechanisms satisfying discounted differential privacy on smart-meter measurement time-series 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 |