|
on Utility Models and Prospect Theory |
| By: | Soetevent, Adriaan; Zhou, L. (Groningen University) |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:gro:rugsom:14022-eef&r=upt |
| By: | Masako Ikefuji (University of Southern Denmark, Denmark); Roger Laeven (University of Amsterdam, the Netherlands); Jan Magnus (VU University Amsterdam, the Netherlands); Chris Muris (Simon Fraser University, Canada) |
| Abstract: | An expected utility based cost-benefit analysis is in general fragile to its distributional assumptions. We derive necessary and sufficient conditions on the utility function of the expected utility model to avoid this. The conditions ensure that expected (marginal) utility remains finite also under heavy-tailed distributional assumptions. Our results are context-free and are relevant to many fields encountering catastrophic risk analysis, such as, perhaps most noticeably, insurance and risk management. |
| Keywords: | Expected utility, Catastrophe, Cost-benefit analysis, Risk management, Power utility, Exponential utility, Heavy tails |
| JEL: | D61 D81 G10 G20 |
| Date: | 2014–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140133&r=upt |
| By: | Anke Gerber (University of Hamburg, Germany); Kirsten I.M. Rohde (Erasmus University Rotterdam, the Netherlands) |
| Abstract: | We propose a utility representation for preferences over risky timed outcomes, the weighted temporal utility model. It separates subjective evaluations of outcomes from attitudes towards psychological distance induced by risks and delays. Subjective evaluations of outcomes may depend on the time of receipt. A natural special case of our model arises when decision makers evaluate an outcome according to the extra utility it generates on top of expected baseline consumption, which can be interpreted as the status quo. Thus, deviations from stationarity can be driven by expected changes in baseline consumption, and need not be irrational. Moreover, a decision maker with a weighted temporal utility function can have time-consistent yet non-stationary preferences or stationary yet time-inconsistent preferences. We provide a characterization of our model and propose a non-parametric approach to elicit a weighted temporal utility function. |
| Keywords: | Intertemporal choice, stationarity, time consistency |
| JEL: | D91 D81 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130167&r=upt |
| By: | Adriaan R. Soetevent (University of Groningen, the Netherlands); Liting Zhou (University of Amsterdam, the Netherlands) |
| Abstract: | Given the possibility to modify the probability of a loss, will a profit-maximizing insurer engage in loss prevention or is it in his interest to increase the loss probability? This paper investigates this question. First, we calculate the expected profit maximizing loss probability within an expected utility framework. We then use Köszegi and Rabin's (2006, 2007) loss aversion model to answer the same question for the case where consumers have reference-dependent preferences. Largely independent of the adopted framework, we find that the optimal loss probability is sizable and for many commonly used parameterizations much closer to 1/2 than to 0. Previous studies have argued that granting insurers market power may incentivize them to engage in loss prevention activities, this to the benefit of consumers. Our results show that one should be cautious in doing so because there are conceivable instances where the insurer's interests in modifying the loss probability to against those of consumers. |
| Keywords: | loss modification, expected utility, reference-dependent preferences, insurance |
| JEL: | D11 D42 D81 L12 |
| Date: | 2014–08–21 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140111&r=upt |
| By: | Bas Donkers (Erasmus University Rotterdam); Carlos J.S. Lourenco (Erasmus University Rotterdam); Benedict G.C. Dellaert (Erasmus University Rotterdam); Daniel G. Goldstein (Microsoft Research) |
| Abstract: | In this paper we propose the use of <I>preferred outcome</I> distributions as a new method to elicit individuals' value and probability weighting functions in decisions under risk. Extant approaches for the elicitation of these two key ingredients of individuals' risk attitude typically rely on a long, chained sequence of lottery choices. In contrast, preferred outcome distributions can be elicited through an intuitive graphical interface, and, as we show, the information contained in two preferred outcome distributions is sufficient to identify non-parametrically both the value function and the probability weighting function in rank-dependent utility models. To illustrate our method and its advantages, we run an incentive-compatible lab study in which participants use a simple graphical interface - the Distribution Builder (Goldstein et al. 2008) - to construct their preferred outcome distributions, subject to a budget constraint. Results show that estimates of the value function are in line with previous research but that probability weighting biases are diminished, thus favoring our proposed approach based on preferred outcome distributions. |
| Keywords: | Decision making, risk preference, distribution builder, rank dependent utility, preference elicitation, micro economics |
| JEL: | G02 D81 D83 M39 |
| Date: | 2013–05–08 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130065&r=upt |
| By: | Brogueira, Joao; Schuetze, Fabian |
| Abstract: | This note proves existence of a unique equilibrium in a Lucas (1978) economy when the utility function displays constant relative risk aversion and log dividends follow a normally distributed AR(1) process with positive auto-correlation. In particular, the note provides restrictions on the coefficient of relative risk aversion, the discount factor and the conditional variance of the consumption process that ensure existence of a unique equilibrium. |
| Keywords: | Asset pricing, Exchange economy, Dynamic programming, Equilibrium conditions |
| JEL: | C61 C62 D51 G12 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2015/02&r=upt |
| By: | Vadym Lepetyuk (Bank of Canada, Canada); Christian A. Stoltenberg (University of Amsterdam) |
| Abstract: | The rise in within-group consumption inequality in response to the increase in within-group income inequality over the last three decades in the U.S. is puzzling to expected-utility-based incomplete market models. The two-sided lack of commitment models exhibit too little consumption inequality while the standard incomplete markets models tend to predict too much consumption inequality. We show that a model with two-sided lack of commitment and chance attitudes, as emphasized by prospect theory, can explain the relationship and can avoid the systematic bias of the expected utility models. The chance attitudes, such as optimism and pessimism, imply that the households attribute a higher weight to high and low outcomes compared to their objective probabilities. For realistic values of risk aversion and of chance attitudes, the incentives for households to share the idiosyncratic risk decrease. The latter effect endogenously amplifies the increase in consumption inequality relative to the expected utility model, thereby improving the fit to the data. |
| Keywords: | Consumption Inequality, Prospect Theory, Limited Enforcement, Risk Sharing |
| JEL: | E21 D31 D52 |
| Date: | 2013–08–17 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130124&r=upt |
| By: | Lin Zhao (University of Amsterdam); Sweder van Wijnbergen (University of Amsterdam) |
| Abstract: | We apply utility indifference pricing to solve a contingent claim problem, valuing a connected pair of gas fields where the underlying process is not standard Geometric Brownian motion and the assumption of complete markets is not fulfilled. First, empirical data are often characterized by time-varying volatility and fat tails; therefore we use Gaussian GAS (Generalized AutoRegressive Score) and GARCH models, extending them to Student's t-GARCH and t-GAS. Second, an important risk (reservoir size) is not hedgeable. Thus markets are incomplete which also makes preference free pricing impossible and thus standard option pricing inapplicable. Therefore we parametrize the investor's risk preference and use utility indifference pricing techniques. We use Lease Square Monte Carlo simulations as a dimension reduction technique. Moreover, an investor often only has an approximate idea of the true probabilistic model underlying variables, making model ambiguity a relevant problem. We show empirically how model ambiguity affects project values, and importantly, how option values change as model ambiguity gets resolved in later phases of the projects considered. We show that traditional valuation approaches will consistently underestimate the value of project flexibility and in general lead to overly conservative investment decisions in the presence of time dependent stochastic structures. |
| Keywords: | real options, time varying volatility and fat tails, GAS models, model ambiguity, decision making in incomplete markets, utility indifference pricing |
| JEL: | C61 D81 G01 G31 G34 Q40 |
| Date: | 2014–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140149&r=upt |
| By: | Keith Marzilli Ericson; Jawwad Noor |
| Abstract: | Delay functions, which vary timing of rewards but fix the money dimension, can elicit the form of discount functions with minimal assumptions. We present a general theorem that characterizes the set of discount functions and utility indices compatible with any 'regular' preference. We provide conditions to test for separable discounted utility (SDU). We elicit individual delay functions for a range of amounts and time horizons. When we impose SDU assumptions, we classify more than half our analysis sample as exponential discounters. However, we reject SDU assumptions for 68% of the sample in favor of magnitude-dependent discounting with time distortion. |
| JEL: | D01 D03 D9 D91 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21095&r=upt |
| By: | Martin Koudstaal (University of Amsterdam); Randolph Sloof (University of Amsterdam, the Netherlands); Mirjam van Praag (Copenhagen Business School, Denmark) |
| Abstract: | Theory predicts that entrepreneurs have distinct attitudes towards risk and uncertainty, but empirical evidence is mixed. To better understand the unique behavioral characteristics of entrepreneurs and the causes of these mixed results, we perform a large ‘lab-in-the-field’ experiment comparing entrepreneurs to managers – a suitable comparison group – and employees (n = 2288). The results indicate that entrepreneurs perceive themselves as less risk averse than managers and employees, in line with common wisdom. However, when using experimental incentivized measures, the differences are subtler. Entrepreneurs are only found to be unique in their lower degree of loss aversion, and not in their risk or ambiguity aversion. This combination of results might be explained by our finding that perceived risk attitude is not only correlated to risk aversion but also to loss aversion. Overall, we therefore suggest using a broader definition of risk that captures this unique feature of entrepreneurs; their willingness to risk losses. |
| Keywords: | Entrepreneurs, managers, risk aversion, loss aversion, ambiguity aversion, lab-in- the field experiment |
| JEL: | L26 C93 D03 |
| Date: | 2014–10–17 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140136&r=upt |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We study a rational expectations' competitive equilibrium in a production economy, i.e., a system of prices at which firms' profit maximizing production decisions and individuals' preferred affordable consumption choices equate supply and demand in every market. We derive the equilibrium price of the firm and the equilibrium short term interest rate, the optimal per capita consumption in society, as well as the risk premium on equity. First a simple linear production technology with constant coefficients is studied, then a more general technology, and finally a general production economy with recursive utility is analyzed by the use of the stochastic maximum principle. While the two first models can not explain the empirics well using conventional preferences, the latter model is found to be much more promising in this regard. Wa also demonstrate a simple proof for the ICAPM. |
| Keywords: | Equity risk premium; production economy; recursive utility; CAPM; CCAPM; ICAPM |
| JEL: | D51 D53 D90 E21 G10 G12 |
| Date: | 2015–04–10 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2015_015&r=upt |
| By: | Arantza Estévez-Fernández (VU University Amsterdam); Peter Borm (Tilburg University, the Netherlands); M. Gloria Fiestras-Janeiro (Universidade de Vigo, Spain) |
| Abstract: | In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalitional merge convex and ordinal convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the NTU-adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games. |
| Keywords: | NTU-bankruptcy problem, NTU-bankruptcy game, Coalitional merge convexity, Ordinal convexity, Compromise stability, Core cover, Adjusted proportional rule |
| JEL: | C71 |
| Date: | 2014–03–04 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140030&r=upt |
| By: | Audrey Hu (University of Amsterdam, the Netherlands); Liang Zou (University of Amsterdam, the Netherlands) |
| Abstract: | We analyze sequential Dutch and Vickrey auctions where risk averse, or risk preferring, bidders may have heterogeneous risk exposures. We derive and characterize a pure strategy equilibrium of both auctions for arbitrary number of identical objects. A sufficient, and to certain extent necessary, condition for this result is that bidders' marginal utilities are log-submodular in income and type. We then show that when bidders are risk averse (preferring), the equilibrium price sequences should be downward (upward) drifting, and in each period the conditional expected revenue is higher (lower) in the Dutch than in the Vickrey sequential auctions. In particular, the "declining price anomaly" is perfectly consistent with nonincreasing absolute risk aversion when bidders have exposures to background risk. |
| Keywords: | sequential auction, background risk, risk preferences, declining prices, log-submodularity |
| JEL: | D44 D82 |
| Date: | 2014–10–20 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140139&r=upt |
| By: | Hooi Hooi Lean (Universiti Sains, Malaysia;); Michael McAleer (National Tsing Hua University, Taiwan; Erasmus University Rotterdam, The Netherlands; and Complutense University of Madrid, Spain) |
| Abstract: | This paper examines risk-averse and risk-seeking investor preferences for oil spot and futures prices by using the mean-variance (MV) criterion and stochastic dominance (SD) approach. The MV findings cannot distinguish between the preferences of spot and futures markets. However, the SD tests show that spot dominates futures in the downside risk, while futures dominate spot in the upside profit. On the other hand, the SD findings suggest that spot dominates futures in downside risk, while futures dominate spot in upside profit. Risk-averse investors prefer investing in the spot index. Risk seekers are attracted to the futures index to maximize their expected utility but not expected wealth in the entire period, as well as for both the OPEC and Iraq War sub-periods. The SD findings show that there is no arbitrage opportunity between the spot and futures markets, and these markets are not rejected as being efficient. |
| Keywords: | Stochastic dominance, mean-variance, risk averter, risk seeker, futures market, spot market |
| JEL: | C14 G12 G15 |
| Date: | 2013–09–05 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130132&r=upt |