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on Utility Models and Prospect Theory |
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Issue of 2019‒09‒16
twenty papers chosen by |
| By: | Bernardo D'Auria; Jos\'e Antonio Salmer\'on |
| Abstract: | Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of insider information. That is, we assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy. For the latter case we obtain an optimal strategy different from the one computed in Pikovsky and Karatzas. We give various examples for which the insider information create arbitrage, and for which the logarithmic maximization problem is bounded or unbounded. We conclude with an interesting result, showing that the insider information may not lead to any arbitrage. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.03430&r=all |
| By: | Silvia Albrizio (Yonsei University) |
| Abstract: | In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization. |
| Keywords: | Decision making, Duality, Games, Incomplete preferences, Utility representation, Vector outcomes. |
| JEL: | C02 C72 D01 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2019rwp-146&r=all |
| By: | Kerem Ugurlu |
| Abstract: | We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space of continuous paths $\O$. We take that the uncertainty set resides in compact sets that are time dependent. In this framework, we solve the robust optimization problem with logarithmic, power and exponential utility functions, explicitly. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.05335&r=all |
| By: | J\"orn Sass; Dorothee Westphal |
| Abstract: | In this paper we investigate a utility maximization problem with drift uncertainty in a continuous-time Black--Scholes type financial market. We impose a constraint on the admissible strategies that prevents a pure bond investment and we include uncertainty by means of ellipsoidal uncertainty sets for the drift. Our main results consist in finding an explicit representation of the optimal strategy and the worst-case parameter and proving a minimax theorem that connects our robust utility maximization problem with the corresponding dual problem. Moreover, we show that, as the degree of model uncertainty increases, the optimal strategy converges to a generalized uniform diversification strategy. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.01830&r=all |
| By: | Christopher P. Chambers; Federico Echenique; Nicolas Lambert |
| Abstract: | We study preferences recovered from finite choice experiments and provide sufficient conditions for convergence to a unique underlying `true' preference. Our conditions are weak, and therefore valid in a wide range of economic environments. We develop applications to expected utility theory, choice over consumption bundles, menu choice or intertemporal consumption. Our framework unifies the revealed preference tradition with models that allow for errors. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.05457&r=all |
| By: | Aleksandr Alekseev (Economic Science Institute, Chapman University) |
| Abstract: | I study the effect of task difficulty on workers' effort and compare it to the effect of monetary rewards in an incentivized lab experiment. I find that task difficulty has an inverse-U effect on effort, and that this effect is quantitatively large when compared to the effect of conditional monetary rewards. Difficulty acts as a mediator of monetary rewards: conditional rewards are most effective at the intermediate or high levels of difficulty. I show that the inverse-U pattern of effort response to difficulty is not consistent with the Expected Utility model but is consistent with the Rank-Dependent Utility model that allows for non-linear probability weighting. I structurally estimate the model and find that it successfully captures the treatment effects observed in the data. I discuss the implications of my findings for the design of optimal incentive schemes for workers and modeling effort. |
| Keywords: | Incentives; Task difficulty; Monetary rewards; Effort Provision; Risk preferences; Probability weighting |
| JEL: | C91 D91 D81 J20 J33 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:19-21&r=all |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics); Bjerksund, Petter (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | With reference to funds established for the benefits of the public at large, a university endowment, or other similar sovereign wealth fund, we demonstrate that the optimal extraction rate from the fund is significantly smaller than the expected real rate of return on the underlying fund. We consider the situation where the influx to the fund has stopped, it is in a steady state, and is invested broadly in the international financial markets. The optimal spending rate secures that the fund is a perpetuity, i.e., it will last 'forever', where the real value of the fund after payments is stationary, while spending according to the expected rate of return will deplete the fund with probability 1. Optimal portfolio choice and spending are then inconsistent. Our conclusions are contrary to the recommendations of an expert panel to the Norwegian Government Pension Fund Global, as well as at odds with part of the extant literature on the management of endowments of universities. |
| Keywords: | Optimal extraction rate; endowment funds; expected utility; recursive utility |
| JEL: | D51 D53 D90 E21 G10 G12 |
| Date: | 2019–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2019_007&r=all |
| By: | David M\"uller; Yurii Nesterov; Vladimir Shikhman |
| Abstract: | We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to natural probabilistic interpretations of the iteration steps. As illustration we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming naturally adjusts demand within a consumption cycle. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.05591&r=all |
| By: | Adam Gorajek (Reserve Bank of Australia) |
| Abstract: | Economists usually inform policymakers with conclusions that come from studying the conditional expectation, i.e. arithmetic mean, of some potential outcome. But there are other means to study, from the same 'quasilinear' family. And they can support very different conclusions. In trade research, for instance, studying other means can transform the perceived roles of colonial history, geography, and trade wars. In wages research, studying other means can reverse perceived earnings differentials between groups. Similar scenarios will be common in other tasks of policy evaluation and forecasting. To choose means well I propose selection criteria, which also consider options that are outside of the quasilinear family, such as quantiles. Optimal choices are application-specific and ideally accommodate the preferences of the relevant policymaker. In the wages case, policymaker aversion to inequality makes it sensible to reject the arithmetic mean for another quasilinear one. |
| Keywords: | policy evaluation; forecasting; quasilinear mean; expected utility; loss function; power transformation; gravity model; inverse hyperbolic sine |
| JEL: | C10 F10 J30 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:rba:rbardp:rdp2019-08&r=all |
| By: | Michail Anthropelos; Tim J. Boonen |
| Abstract: | We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents' strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents' bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.01739&r=all |
| By: | Fabian Gouret (Université de Cergy-Pontoise, THEMA) |
| Abstract: | This paper uses data from the 2004 pre-election survey of the American National Election Study to test empirically different ways of incorporating a valence parameter into a Downsian utility function. We call particular attention to the problem of interpersonal incomparability of responses to the liberal-conservative scale, and use the Aldrich-McKelvey’s pathbreaking method to obtain accurate distances between respondents and candidates, the key regressors. We find that the utility function the most supported by the empirical evidence, the intensity valence utility function, is the one which permits to make the better predictions for the 2004 presidential election. We also consider counterfactual analyses wherein we test if Bush, the candidate with the highest intensity valence, has dominant strategies which would have insured him to obtain a majority of the popular vote. According to the theory, it is known that the candidate with the highest intensity valence does not have such dominant strategies if the distribution of voters in the policy space is too heterogenous. Nevertheless, we show the distribution of voters in 2004 is sufficiently homogenous for Bush to have dominant strategies. |
| Keywords: | spatial models of voting, valence, survey, Aldrich-McKelvey scaling. |
| JEL: | D72 C81 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2019-10&r=all |
| By: | Shivani Taneja (University of Essex) |
| Abstract: | The gender gap in attaining a university qualification has gradually narrowed in Britain and this has motivated the evaluation of gender differences in non-pecuniary returns of education. Therefore, this paper explores the trends in job utility of workers, measured by subjective self-evaluation of satisfaction scores from work. The data shows that while female workers experience higher job utility compared to men during the survey period, male workers are reporting higher utility in recent years, resulting in narrowing gender gap in job utility. Logistic regression models are used to understand the factors contributing to this gender gap. The results suggest that education is unlikely to contribute to this trend whereas unemployment has a small contribution to the emerging pattern. Furthermore, the results show that job utility of male workers is more cyclically sensitive compared to female workers as stalling unemployment during an economic downturn affects men more than women. |
| Keywords: | Job satisfaction, Unemployment, United Kingdom |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:sek:iacpro:9010643&r=all |
| By: | Cars Hommes; Kostas Mavromatis; Tolga Ozden; Mei Zhu |
| Abstract: | We introduce the concept of behavioral learning equilibrium (BLE) into a high dimensional linear framework and apply it to the standard New Keynesian model. For each endogenous variable, boundedly rational agents use a simple, but optimal AR(1) forecasting rule with parameters consistent with the observed sample mean and autocorrelation of past data. The main contributions of our paper are fourfold: (1) we derive existence and stability conditions of BLE in a general linear framework, (2) we provide a general method for Bayesian likelihood estimation of BLE, (3) we estimate the baseline NK model based on U.S. data and show that the relative model fit is better under BLE than REE, (4) we analyze optimal monetary policy under BLE and show that it differs from REE. In particular, we find that the transmission channel of monetary policy is stronger under BLE at the estimated parameter values. |
| Keywords: | Bounded rationality; Behavioral learning equilibrium; Adaptive learning; behavioral New Keynesian macro-model; Monetary Policy |
| JEL: | C11 E62 D83 D84 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:dnb:dnbwpp:654&r=all |
| By: | Gibbs, Christopher G.; McClung, Nigel |
| Abstract: | We provide suffcient conditions for when a rational expectations structural model predicts bounded responses of endogenous variables to forward guidance announcements. The conditions coincide with a special case of the well-known (E)xpectation-stability conditions that govern when agents can learn a Rational Expectations Equilibrium. Importantly, we show that the conditions are distinct from the determinacy conditions. We show how the conditions are useful for diagnosing the features of a model that contribute to the Forward Guidance Puzzle and reveal how to construct well-behaved forward guidance predictions in standard medium-scale DSGE models. |
| JEL: | E31 E32 E52 D84 D83 |
| Date: | 2019–09–10 |
| URL: | http://d.repec.org/n?u=RePEc:bof:bofrdp:019&r=all |
| By: | Tommaso Lando; Lucio Bertoli-Barsotti |
| Abstract: | We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a decision maker's preferences in terms of risk aversion and may be used in those situations in which a strong order does not have enough discriminative power, whilst a weaker one is poorly representative of some classes of decision makers. In particular, we focus on the class of power distortion functions, yielding power-distorted stochastic dominance, which seems to be particularly appealing owing to its computational simplicity and some interesting statistical interpretations. Finally, we characterize distorted stochastic dominance in terms of distortion functions yielding isotonic classes of distorted expectations. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.04767&r=all |
| By: | Alberto Chong (Department of Economics, Andrew Young School of Policy Studies, Georgia State University, USA); Joan J. Martínez (University of California, Berkeley, USA) |
| Abstract: | We provide empirical evidence that supports a causal link from education to risk aversion when using representative data from representative surveys and artefactual or lab-in-the field experiments in Lima, Peru. We employ three standard experimental measures of risk aversion and find that each of them is positively correlated with years of education. We suggest that this relationship may be causal as we take advantage of an identification strategy that exploits a national law enacted in order to incentivize the construction of new schools in Lima, which allows us to provide evidence that more education may increase risk aversion. Our findings are further confirmed when applying a broad set of robustness tests. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:ays:ispwps:paper1917&r=all |
| By: | Nathalie Gimenes; Emmanuel Guerre |
| Abstract: | The paper proposes a sieve quantile regression approach for first-price auctions with symmetric risk-neutral bidders under the independent private value paradigm. It is first shown that a private value quantile regression model generates a quantile regression for the bids. The private value quantile regression can be easily estimated from the bid quantile regression and its derivative with respect to the quantile level. A new local polynomial technique is proposed to estimate the latter over the whole quantile level interval. Plug in estimation of functionals is also considered, as needed for the expected revenue or the case of CRRA risk-averse bidders, which is amenable to our framework. A quantile regression analysis to USFS timber is found more appropriate than the homogenized bid methodology and illustrates the contribution of each explanatory variables to the private value distribution. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.05542&r=all |
| By: | Ravi Bansal; Mariano Max Croce; Wenxi Liao; Samuel Rosen |
| Abstract: | Focusing on both micro and aggregate U.S. data, we show the existence of a significant link between aggregate uncertainty and reallocation of resources away from R&D-intensive capital. This link is important because a decrease in the aggregate share of R&D-oriented capital forecasts lower medium-term growth. In a multi-sector production economy in which (i) growth is endogenously supported by risky R&D investments, and (ii) the representative agent is volatility-risk averse and has access to other safer technologies that do not support growth, uncertainty shocks have a first-order negative impact on medium-term growth and welfare. |
| JEL: | E3 E6 G18 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26248&r=all |
| By: | Yongyang Cai; William Brock; Anastasios Xepapadeas; Kenneth Judd |
| Abstract: | We build a novel stochastic dynamic regional integrated assessment model (IAM) of the climate and economic system including a number of important climate science elements that are missing in most IAMs. These elements are spatial heat transport from the Equator to the Poles, sea level rise, permafrost thaw and tipping points. We study optimal policies under cooperation and noncooperation between two regions (the North and the Tropic-South) in the face of risks and recursive utility. We introduce a new general computational algorithm to find feedback Nash equilibrium. Our results suggest that when the elements of climate science are ignored, important policy variables such as the optimal regional carbon tax and adaptation could be seriously biased. We also find the regional carbon tax is significantly smaller in the feedback Nash equilibrium than in the social planner's problem in each region, and the North has higher carbon taxes than the Tropic-South. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.04009&r=all |
| By: | Mirzaei, Farzad; Mahdavi, Sadegh; Bayat, Alireza |
| Abstract: | Security Constraint Unit commitment (SCUC) is one of the challenging economic problem of the power utilities due to the ON and OFF status of the units. Indeed, in SCUC we should determine the status of the units for the day-ahead horizon. SCUC is a mixed-integer linear problem (MILP), which is hard to solve. Hence, in this paper, a new evolutionary algorithm, known as the multiverse optimization algorithm is developed to solve the problem. |
| Keywords: | Security constrained unit commitment, economic operation, evolutionary algorithm, optimization |
| JEL: | A1 G0 H0 L0 L9 P0 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95894&r=all |