nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2016‒02‒04
thirteen papers chosen by
Alexander Harin
Modern University for the Humanities

  1. Robust Optimal Risk Sharing and Risk Premia in Expanding Pools By Thomas Knispel; Roger J. A. Laeven; Gregor Svindland
  2. Convex duality for stochastic differential utility By Anis Matoussi; Hao Xing
  3. Portfolio optimization under dynamic risk constraints By Imke H\"ofers; Ralf Wunderlich
  4. Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift By J\"orn Sass; Dorothee Westphal; Ralf Wunderlich
  5. Smooth preferences, symmetries and expansion vector fields By A. Mantovi
  6. Behavioural Drivers of Stocking Rate Decisions in Less Favoured Areas By McCormack, Michele; O’Donoghue, Cathal; Loughrey, Jason
  7. Risk sharing in a world economy with uncertainty shocks By Kollmann, Robert
  8. Estimating utility-consistent poverty in Madagascar, 2001.10 By David Stifel; Tiaray Razafimanantena; Faly Rakotomanana
  9. Some $\lambda$-separable Frisch demands with  utility functions By Ligon, Ethan
  10. All \lambda-separable Frisch demands and corresponding utility functions By Ligon, Ethan
  11. Herding and Contrarian Behavior in Financial Markets : An Experimental Analysis By Park, Andreas; Sgroi, Daniel
  12. Rankings and Risk-Taking in the Finance Industry By Michael Kirchler; Florian Lindner; Utz Weitzel
  13. Inequity-averse preferences in general equilibrium By Rodrigo A. Velez

  1. By: Thomas Knispel; Roger J. A. Laeven; Gregor Svindland
    Abstract: We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools.
    Date: 2016–01
  2. By: Anis Matoussi; Hao Xing
    Abstract: This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment problem is identified without assuming several technical conditions on market model, utility specification, and agent's admissible strategy. Meanwhile the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the "least favorable" completion of the market.
    Date: 2016–01
  3. By: Imke H\"ofers; Ralf Wunderlich
    Abstract: We consider an investor faced with the classical portfolio problem of optimal investment in a log- Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies which reduce a dynamic shortfall risk measure. For continuous and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is quite small while the risk is reduced considerably. We also investigate discretization effects and the loss in performance if trading is possible at discrete time points only.
    Date: 2016–02
  4. By: J\"orn Sass; Dorothee Westphal; Ralf Wunderlich
    Abstract: This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing stock returns and expert opinions. The latter provide unbiased estimates on the current state of the drift at discrete points in time. The optimal trading strategy of investors maximizing expected logarithmic utility of terminal wealth depends on the filter which is the conditional expectation of the drift given the available information. We state filtering equations to describe its dynamics for different information settings. Between expert opinions this is the Kalman filter. The conditional covariance matrices of the filter follow ordinary differential equations of Riccati type. We rely on basic theory about matrix Riccati equations to investigate their properties. Firstly, we consider the asymptotic behaviour of the covariance matrices for an increasing number of expert opinions on a finite time horizon. Secondly, we state conditions for the convergence of the covariance matrices on an infinite time horizon with regularly arriving expert opinions. Finally, we derive the optimal trading strategy of an investor. The optimal expected logarithmic utility of terminal wealth, the value function, is a functional of the conditional covariance matrices. Hence, our analysis of the covariance matrices allows us to deduce properties of the value function.
    Date: 2016–01
  5. By: A. Mantovi
    Abstract: Tyson (2013) introduces the notion of symmetry vector field for a smooth preference relation, and establishes necessary and sufficient conditions for a vector field on consumption space to be a symmetry vector field. The structure of a such a condition is discussed on both geometric and economic grounds. It is established that symmetry vector fields do commute (i.e. have vanishing Lie bracket) for additive and joint separability. The marginal utility of money is employed as a normalization of the expansion vector field (Mantovi (2013) which results in the fundamental (expansion-) symmetry vector field. Finally, a characterization of symmetry vector fields is given in terms of their action on the distance function, and a pattern of complete response is discussed for additive preferences. Examples of such constructions are explicitly worked out. Potential implications of the results are discussed.
    Keywords: Utility Function, Symmetry, Separability, Vector Field, Expansion Path, Distance Function
    JEL: D01 D04 D11
    Date: 2016
  6. By: McCormack, Michele; O’Donoghue, Cathal; Loughrey, Jason
    Abstract: In this paper we use a natural experiment to investigate the behavioural response of Irish Cattle farmers to historical policy incentives. In particular we are interested in the period 2001 – 2005 when Less Favoured Area payments were decoupled from production and other subsidy payments available to all farmers remained coupled. The decoupling of the Less Favoured Areas payment provides an exogenous source of variation that gives us unique opportunity for policy evaluation. Researchers rarely observe the effects of a policy change on those affected and those not affected since in almost all cases a policy change affects all. We adopt an ordinal Utility maximization consumer choice framework where individuals make decisions in relation to consumption and leisure. Under our model of utility maximization the expected market gross margin is positively associated with livestock intensity. We identify a non-linear relationship between direct coupled payments and livestock intensity which suggests that high payments incentivise farmers towards extensification. Using a Difference in Difference with propensity score matching we find that there were substantial differences in the behavioural responses of both groups. Farms where payments remained fully coupled adapted their stocking rate decisions in a way that reflects both learning and rationality more significantly than farms where part of their payment was decoupled.
    Keywords: Agricultural and Food Policy,
    Date: 2015
  7. By: Kollmann, Robert (European Centre for Advanced Research in Economics and Statistics (ECARES))
    Abstract: This paper analyzes the effects of output volatility shocks and of risk appetite shocks on the dynamics of consumption, trade flows and the real exchange rate, in a two-country world with recursive preferences and complete financial markets. When the risk aversion coefficient exceeds the inverse of the intertemporal substitution elasticity, then an exogenous rise in a country’s output volatility triggers a wealth transfer to that country, in equilibrium; this raises its consumption, lowers its trade balance and appreciates its real exchange rate. The effects of risk appetite shocks resemble those of volatility shocks. In a recursive preferences-complete markets framework, volatility and risk appetite shocks account for a noticeable share of the fluctuations of net exports, net foreign assets and the real exchange rate. These shocks help to explain the high empirical volatility of the real exchange rate and the disconnect between relative consumption growth and the real exchange rate.
    JEL: F31 F32 F36 F41 F43
    Date: 2015–11–01
  8. By: David Stifel; Tiaray Razafimanantena; Faly Rakotomanana
    Abstract: We adapt the standardized Poverty Line Estimation Analytical Software.PLEASe computer code stream based on Arndt and Simler.s (2010) utility-consistent approach to measuring consumption poverty in order to analyse poverty in Madagascar in 2001, 2005, and 2010. This paper documents how the utility-consistent approach to inter-temporal and spatial deflation differs from the approach undertaken by the national statistical office to produce the official poverty estimates and how the trends in these estimates differ substantially. Further, we illustrate the importance of addressing extreme values for calculating unit prices, and how to handle redistricting when conducting revealed preference tests of the utility-consistency of not only regionally estimated poverty lines (i.e. do the consumption patterns in other spatial domains cost no less than the own-domain consumption patterns when both are evaluated at owndomain prices), but also of poverty lines over time.
    Keywords: poverty measurement, utility-consistent poverty lines, Madagascar
    Date: 2015
  9. By: Ligon, Ethan
    Abstract: We complete the characterization of two Frisch demand systems first developed by \cite{Browning-etal85}, and show that that these systems (i) do not restrict intertemporal substitution; but (ii) imply momentary utility functions which are additively separable in consumption. These utility functions turn out to take the well-known exponential and Stone-Geary forms.
    Keywords: Social and Behavioral Sciences, Frisch demands, separability, intertemporal elasticity of substitution
    Date: 2016–01–27
  10. By: Ligon, Ethan
    Abstract: Frisch demands depend on prices and a multiplier \(\lambda\)associated with the consumer's budget constraint. The case in whichdemands or expenditures are separable in $\lambda$ is the case ofgreatest empirical interest, since in this case latent variablemethods can be adopted to control for consumer wealth when estimatingdemands. Subject only to standard, modest, regularity conditions, we provide a completecharacterization of all Frisch demand systems and of the utilityfunctions that rationalize these demand systems when either quantitiesdemanded or consumption expenditures is separable in $\lambda$. Quantities demanded are \(\lambda\)-separable if and only if therationalizing utility function is additively separable in thesequantities. In contrast, expenditures are \(\lambda\)-separable ifand only if marginal utilities for these expenditures belong to one oftwo simple parametric families. With $n$ goods, the first family has$2n$ parameters, and corresponds to Houthakker's "direct addilog"utility function. The second family has $3n$ parameters and is new.It corresponds to a family of utility functions which have Stone-Gearyutility as a limiting case.
    Keywords: Social and Behavioral Sciences, Frisch demands, separability, Pexider equations
    Date: 2016–01–27
  11. By: Park, Andreas (University of Toronto); Sgroi, Daniel (University of Warwick)
    Abstract: We analyze and confirm the existence and extent of rational informational herding and rational informational contrarianism in a financial market experiment, and compare and contrast these with equivalent irrational phenomena. In our study, subjects generally behave according to benchmark rationality. Traders who should herd or be contrarian in theory are the signicant sources of both within the data. Correcting for subjects who can be identified as less rational increases our ability to predict herding or contrarian behavior considerably.
    Keywords: Herding ; Contrarianism ; Informational Efficiency ; Experiments JEL classification numbers: C91 ; D82 ; G14
    Date: 2016
  12. By: Michael Kirchler; Florian Lindner; Utz Weitzel
    Abstract: Rankings are a pervasive feature of the finance industry. Although they have no di- rect monetary consequences, rankings provide utility for intrinsic (positive self-image) and extrinsic (status) reasons. We recruit a unique subject pool of 204 financial professionals and investigate how anonymous rankings influence risk-taking in investment decisions. We find that rankings increase risk-taking because of financial professionals? desire for positive self-image. This particularly applies to underperformers, who take the highest risks. Incentivizing rankings monetarily does not further increase risk-taking. In a comparative study with 432 students we find that student behavior is not driven by rankings.
    Keywords: Experimental finance, behavioral finance, rank incentives, rankings, financial professionals, investment game, framed field experiment, tournament incentives
    JEL: G02 G11 D03 C93
    Date: 2016–01
  13. By: Rodrigo A. Velez (Texas A&M University, Department of Economics)
    Abstract: We study the stability with respect to the introduction of opportunity-based inequity aversion a la Dufwenberg et. al (2011) of three welfare properties satisfied by competitive equilibria in self-regarding economies: (i) Pareto efficiency may not be a stable property; (ii) undomination with respect to income redistribution is a stable property whenever the marginal indirect utility of income has no extreme variations; and (iii) generically (endowment-wise) market-constrained efficiency is a stable property.
    Keywords: inequity aversion, general equilibrium
    JEL: D63 C72
    Date: 2016–01–11

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