
on Utility Models and Prospect Theory 
By:  Guilherme Lichand; Juliette Thibaud 
Abstract:  This paper uses a labinthefield experiment in Malawi to document two new facts about how parents share resources with their children over time. First, for almost a third of study participants, the further in the future consumption is, the more generous are parents’ plans to share it with their children. Second, many participants revise those plans as consumption gets closer, reallocating from children towards themselves – even when consumption is still in the future. None of these patterns can be accounted for by presentbias. Instead, both are consistent with a relevant share of parents discounting their future utility of consumption to a greater extent than that of their children. We document that parents characterized by such asymmetric geometric discounting display sizable preference reversals every period, a phenomenon we denote parentbias. We find that, despite ambitious plans, those parents actually allocate less to their children in the present than other parents, and that such preferences predict underinvestment in children outside the lab just as much as quasihyperbolic discounting. Commitment devices designed for presentbias do not mitigate parentbias. Our findings provide a new explanation for underinvestment in children and inform the design of new interventions to address it. 
Keywords:  Time preferences, preference reversals, children’s human capital 
JEL:  C91 D13 E24 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:369&r=all 
By:  Atilla Aras 
Abstract:  In this paper, the solution of the equity premium puzzle was given. First, the ArrowPratt measure of relative risk aversion for detecting the risk behavior of investors was questioned, and then a new tool was developed to study the risk behavior of investors. This new tool in the new formulated model was tested for the equity premium puzzle for a solution. The results show that the calculated value of the coefficient of relative risk aversion is 2.201455 which is compatible with the empirical studies and as investors who invest in riskfree asset place disutility on the not sure wealth value, investors who invest in equity place utility on the not sure wealth value. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.05458&r=all 
By:  Gregorio Curello; Ludvig Sinander 
Abstract:  An agent privately observes a technological breakthrough that expands utility possibilities, and must be incentivised to disclose it. The principal controls the agent's utility over time. Optimal mechanisms keep the agent only just willing to disclose promptly. In an important case, a deadline mechanism is optimal: absent disclosure, the agent enjoys an efficient utility before a deadline, and an inefficiently low utility afterwards. In general, optimal mechanisms feature a (possibly gradual) transition from the former to the latter. Even if monetary transfers are permitted, they may not be used. We apply our results to the design of unemployment insurance schemes. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.10090&r=all 
By:  Peter Bank; Yan Dolinsky 
Abstract:  We consider the Bachelier model with information delay where investment decisions can be based only on observations from $H>0$ time units before. Utility indifference prices are studied for vanilla options and we compute their nontrivial scaling limit for vanishing delay when risk aversion is scaled liked $A/H$ for some constant $A$. Using techniques from [7], we develop discretetime duality for this setting and show how the relaxed form of martingale property introduced by [9] results in the scaling limit taking the form of a volatility control problem with quadratic penalty. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.05023&r=all 
By:  Connor, G.; Li, S.; Linton, O. 
Abstract:  This paper develops a twostep semiparametric methodology for portfolio weight selection for characteristicsbased factortilt and factortiming investment strategies. We build upon the expected utility maximization framework of Brandt (1999) and Aïtsahalia and Brandt (2001). We assume that assets’ returns obey a characteristicsbased factor model with timevarying factor risk premia as in Li and Linton (2020). We prove under our returngenerating assumptions that in a market with a large number of assets, an approximately optimal portfolio can be established using a twostep procedure. The first step finds optimal factormimicking subportfolios using a quadratic objective function over linear combinations of characteristicsbased factor loadings. The second step dynamically combines these factormimicking subportfolios based on a timevarying signal, using the investor’s expected utility as the objective function. We develop and implement a twostage semiparametric estimator. We apply it to CRSP (Center for Research in Security Prices) and FRED (Federal Reserve Economic Data) data and find excellent insample and outsample performance that are consistent with investors’ risk aversion levels. 
Keywords:  Portfolio management, Single index, GMM 
JEL:  C14 G11 
Date:  2020–11–11 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:20103&r=all 
By:  Guohui Guan; Zongxia Liang; Fengyi Yuan 
Abstract:  This paper studies the retirement decision, optimal investment and consumption strategies under habit persistence for an agent with the opportunity to design the retirement time. The optimization problem is formulated as an interconnected optimal stopping and stochastic control problem (StoppingControl Problem) in a finite time horizon. The problem contains three state variables: wealth $x$, habit level $h$ and wage rate $w$. We aim to derive the retirement boundary of this "wealthhabitwage" triplet $(x,h,w)$. The complicated dual relation is proposed and proved to convert the original problem to the dual one. We obtain the retirement boundary of the dual variables based on an obstacletype free boundary problem. Using dual relation we find the retirement boundary of primal variables and feedback forms of optimal strategies. We show that if the socalled "de facto wealth" exceeds a critical proportion of wage, it will be optimal for the agent to choose to retire immediately. In numerical applications, we show how "de facto wealth" determines the retirement decisions and optimal strategies. Moreover, we observe discontinuity at retirement boundary: investment proportion always jumps down upon retirement, while consumption may jump up or jump down, depending on the change of marginal utility. We also find that the agent with higher standard of life tends to work longer. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.10166&r=all 
By:  Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Li, Hanwu (Center for Mathematical Economics, Bielefeld University); Riedel, Frank (Center for Mathematical Economics, Bielefeld University) 
Abstract:  We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent's preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient firstorder conditions for optimality. With the help of a backward equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions. 
Keywords:  HindyHuangKreps preferences, Knightian uncertainty, gexpectation, ambiguity aversion, singular stochastic control 
Date:  2020–11–23 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:641&r=all 
By:  Silvana Pesenti; Qiuqi Wang; Ruodu Wang 
Abstract:  Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result that allows us to convert an optimization of a nonconvex distortion riskmetric with distributional uncertainty to a convex one, leading to great tractability. The key to the unifying equivalence result is the novel notion of closedness under concentration of sets of distributions. Our results include many special cases that are well studied in the optimization literature, including but not limited to optimizing probabilities, ValueatRisk, Expected Shortfall, and Yaari's dual utility under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.04889&r=all 
By:  Thomas Favory (Economics Discipline, Business School, University of Western Australia) 
Abstract:  This paper proves the existence and uniqueness of BertrandNash equilibrium in oligopolies, where each firm may sell multiple substitutes of the same good. Bertrand competition emerges as a limit case when the number of products per firm increases if the consumers’ willingness to pay for products follow a sufficiently slimtailed distribution. In opposition, the double exponential distribution is not slim enough, and firms conserve monopolistic power even for an arbitrarily large number of products per firm. Moreover, the double exponential distribution provides closedform solutions that relate to discrete choice theory. First, a duality with representative consumers helps recover multinomial logit (MNL) demand functions and constant elasticity of substitution (CES) utility functions. Second, the game in which firms sequentially set the quality, then the price of their products, has a unique equilibrium. 
Keywords:  Multiproduct firms, Price competition, Oligopoly, Discrete choice, Product differentiation 
JEL:  D21 D43 L12 L13 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:uwa:wpaper:2024&r=all 
By:  John B. Davis (Department of Economics Marquette University) 
Abstract:  This paper develops a conception of reflexive economic agents as an alternative to the standard utility conception, and explains individual identity in terms of how agents adjust to change in a selforganizing way, an idea developed from Herbert Simon. The paper distinguishes closed equilibrium and open process conceptions of the economy, and argues the former fails to explain time in a beforeandafter sense in connection with Aristotle's sea battle problem. A causal model is developed to represent the process conception, and a structureagency understanding of the adjustment behavior of reflexive economic agents is illustrated using Merton's selffulfilling prophecy analysis. Simon's account of how adjustment behavior has stopping points is then shown to underlie how agents' identities are disrupted and then selforganized, and the identity analysis this involves is applied to the different identity models of Merton, Ross, Arthur, and Kirman. Finally, the selforganization idea is linked to the recent 'preference purification' debate in bounded rationality theory regarding the 'inner rational agent trapped in an outer psychological shell,' and it is argued that the behavior of selforganizing agents involves them taking positions toward their own individual identities. 
Keywords:  reflexivity, Simon, Aristotle identity, selffulfilling prophecy 
JEL:  B11 B25 B41 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:mrq:wpaper:202001&r=all 
By:  Leroux, MarieLouise (Université catholique de Louvain, LIDAM/CORE, Belgium); Pestieau, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium) 
Abstract:  This paper studies the design of the optimal linear taxation of bequests when individuals differ in wage as well as in their risks of both mortality and oldage dependance. We assume that the government cannot distinguish between bequests motives, that is whether bequests resulted from precautionary reasons or from pure joy of giving reasons. Instead, we assume that it only observes the timing of bequests, that is whether they are made early in life or late in life. We show that, if the government is utilitarian, whether the taxation of early bequests should be given priority over the taxation of late bequests depends on the magnitude of insurance and redistributive concerns. While the efficiency concern unambiguously recom mends taxation of early bequests, redistributive concerns yield ambiguous results. This indeterminacy comes from the fact that, in case of late death, the government cannot ob serve the health status of the deceased. Whether the taxation of early bequests should be given priority depends on the specific relationships between wages and both risks of early death and of oldage dependence, as well as on the concavity of the joy of giving utility function. If the government is Rawlsian, it is optimal to tax early bequests if the survival chances of the poorest agents are very low. If they survive, but their chances to remain autonomous are very low, it is then optimal to tax early bequests if the poorest agents con tribute relatively less to the taxation of early bequests than to the taxation of late bequests or if the joy of giving utility is extremely concave. 
Keywords:  Bequest taxation; Long term care; Utilitarianism; Rawlsian welfare criterion; Oldage dependency 
JEL:  H21 H23 I14 
Date:  2020–10–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2020031&r=all 
By:  Flavio Angelini; Katia Colaneri; Stefano Herzel; Marco Nicolosi 
Abstract:  We study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. The estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. We solve the problem via the martingale method and, with a concavification procedure, we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.07871&r=all 
By:  Sampson, C.; Parkin, D.; Devlin, N. 
Abstract:  By convention, values for generic 'preferencebased' measures, such as the EQ5D, are anchored at 1 = full health and 0 = dead. This paper challenges the assumption that anchoring health state values at 'dead = 0' is a necessary condition for values to be used in qualityadjusted life year (QALY) estimation. The authors consider five propositions, using narrative review of the literature and conceptual explication of the problem   anchoring at 'dead' is not required by theories of scale measurement and utility;  calculating QALY gains does not require a distinction between states better than and worse than dead;  costeffectiveness analysis does not require that 'dead' has a value relative to health states;  using 'dead' as an anchor causes problems that make studies difficult to conduct and their results difficult to interpret; and  there are alternative states to 'dead' that exhibit favourable properties for anchoring. There is support for each proposition. Anchoring health state values at dead was an arbitrary choice made early in the development of health state valuation methods. The use of dead as an anchor is unnecessary and undesirable because of the methodological and conceptual issues it causes. The authors conclude that, in valuing health states, researchers should 'drop dead'. 
Keywords:  Measuring and Valuing Outcomes 
JEL:  I1 
Date:  2020–11–01 
URL:  http://d.repec.org/n?u=RePEc:ohe:respap:002308&r=all 
By:  Georg Meran; Markus Siehlow; Christian von Hirschhausen 
Abstract:  This paper applies a microeconomicbased stylized model to identify the optimal modal split of water supply infrastructure in regions of the Global South against the background of the Sustainable Development Goal (SDG) No. 6. We assume a linear city, with some plausible assumptions on income and willingnesstopay, and then calculate the optimal tap density, leading in turn to an optimal modal split between piped and unconnected water consumption. From an economic perspective, not all water users need to be connected to a centralized, pipeline infrastructure, and the nonconnected households should be served by nonmobile or mobile vendors. The analysis is ﬁrstly made for the case of totally inelastic demand functions for simpliﬁcation reasons and afterwards the analysis becomes more complicated and realistic by addressing elastic demand functions which are based on a simpliﬁed version of the StoneGeary utility function. In terms of policy implications, the paper suggests a role for decentral, offgrid solutions to generalized water supply, with a certain role for water vendors. 
Keywords:  Water, Infrastructure, mobile vendors, integrated planning, informal economy 
JEL:  C31 R12 O17 Q25 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1916&r=all 
By:  Lake, A. 
Abstract:  Trying to estimate rational expectations does not usually minimise forecast error when forecasting macroeconomic or financial variables in reality. This is because, with samples of realistic length, optimal feasible forecasts contain conditional biases that reduce forecast variance. I demonstrate this by using penalised factor models to show that statistically simple inflation forecasts, primarily based on past inflation, are optimal even when other relevant financial and economic variables are available. I also show that US household inflation forecasts display many similarities to these simple optimal forecasts, but also contain mistakes that increase forecast error. Therefore a combination of `optimal feasible expectations' and behavioural errors explain US household inflation forecasts. This suggests that optimal feasible expectations, with additional behavioural errors in some cases, could explain forecast formation across economics and finance. 
Keywords:  Forecasting, Expectations, Uncertainty, Shrinkage, Ination, Nominal Rigidities, Factor Models 
JEL:  E37 D84 C53 
Date:  2020–11–11 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:20105&r=all 
By:  Petrishcheva, Vasilisa (Heinrich Heine University Düsseldorf); Riener, Gerhard (Düsseldorf Institute for Competition Economics (DICE)); SchildbergHörisch, Hannah (Heinrich Heine University Düsseldorf) 
Abstract:  This paper explores whether loss aversion applies to social image concerns. In a simple model, we combine loss aversion in social image concerns and attitudes towards lying. We then test its predictions in a laboratory experiment. Subjects are first ranked publicly in a social image relevant domain, intelligence. This initial rank serves as withinsubject reference point. After inducing an exogenous change in subjects' rank across treatments, subjects are offered scope for lying to improve their final rank. We find evidence for loss aversion in social image concerns. Subjects who face a loss in social image lie more than those experiencing gains if they sufficiently care about social image and have a reputation to lose. Individuallevel analyses document a discontinuity in lying behavior when moving from rank losses to gains, indicating a kink in the value function for social image. 
Keywords:  loss aversion, social image concerns, lying behavior, laboratory experiment 
JEL:  C91 D91 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp13896&r=all 
By:  Juan Dubra; JeanPierre Benoit; Giorgia Romagnoli 
Abstract:  Incentive compatible mechanisms for eliciting beliefs typically presume that theutilty of money is state independent, or that money is the only argument in utilityfunctions. However, subjects may have nonmonetary objectives that confound themechanisms. In particular, psychologists have argued that people favour bets wheretheir ability is involved over equivalent random bets ña socalled preference for control.We propose a new belief elicitation method that mitigates the control preference. Usingthis method, we determine that under the ostensibly incentive compatiblematchingprobabilities method, our subjects report selfbeliefs 18% higher than their true beliefsin order to increase control. Nonmonetary objectives account for at least 68% of whatwould normally be measured as overconÖdence. Our mechanism can be used to yieldbetter measurements of beliefs in contexts beyond the study of overconÖdence. Ourpaper also contributes to a reÖned understanding of control. We find that control manifests itself only as a desire for betting on doing well; betting on doing badly isperceived as a negative. 
Keywords:  Elicitation, OverconÖdence, Control. Experimental Methods 
JEL:  D3 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:mnt:wpaper:2001&r=all 
By:  Damien Bazin (Université Côte d'Azur; GREDEG CNRS); Naceur Khraief (Tunis Business School) 
Abstract:  Le présent papier explique la décision de suicide, associée à l'agriculteur de coton Bt en Inde, dans le cadre d'un modèle de maximisation d'une fonction d'utilité intertemporelle et conformément aux écrits sur l'économie du suicide. Dans cet article, on affirme que l'incertitude entourant l'efficacité du coton Bt contre les ravageurs était le principal facteur de suicides d'agriculteurs en Inde. L'objectif principal de cet article est de construire un modèle économique de suicide pour examiner les impacts de l'incertitude, associé à la rentabilité du coton Bt, sur le comportement suicidaire des paysans indiens. A cet effet, on a proposé l'extension du modèle de Hamermesh et Soss tout en adoptant l'hypothèse de l'incertitude sur le gain net futur du coton Bt supposé suivre un processus stochastique. A partir de notre modèle, le profit du seuil, audessous duquel un agriculteur se suicide, est déterminé en fonction des paramètres du processus aléatoire. Les effets de variations de ces paramètres sur le profit du seuil sont considérés. Enfin, on tire les conclusions sur les impacts de l'incertitude relative au gain net du coton Bt sur la décision de suicide de l'agriculteur indien. 
Keywords:  Coton OGM, Economie du suicide, Incertitude, Maximisation de l'utilité 
JEL:  Q12 Q16 Q18 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:gre:wpaper:202047&r=all 
By:  Martin, Ian; Ross, Steve 
Abstract:  We study the properties of the yield curve under the assumptions that (i) the fixedincome market is complete and (ii) the state vector that drives interest rates follows a finite discretetime Markov chain. We focus in particular on the relationship between the behavior of the long end of the yield curve and the recovered time discount factor and marginal utilities of a pseudorepresentative agent; and on the relationship between the “trappedness” of an economy and the convergence of yields at the long end. 
Keywords:  yield curve; term structure; recovery theorem; traps; Cheeger inequality; eigenvalue gap 
JEL:  G12 
Date:  2019–12–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:90208&r=all 