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12
Putting Risk in its Proper Place
 American Economic Review
"... This paper examines preferences towards particular lotteries of random wealth variables. The lotteries consist essentially of two basic dislikes: a certain reduction in wealth and adding a zeromean independent noise random variable to the distribution of wealth. We show how concepts such as risk av ..."
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Cited by 14 (4 self)
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This paper examines preferences towards particular lotteries of random wealth variables. The lotteries consist essentially of two basic dislikes: a certain reduction in wealth and adding a zeromean independent noise random variable to the distribution of wealth. We show how concepts such as risk aversion, prudence and temperance can be fully characterized by a preference relation over such lotteries. By nesting these lotteries, we can fully characterize the class of mixedriskaverse preferences, as defined by Caballé and Pomansky (1996).
Portfolio Selection in Multidimensional General and Partial Moment Space
, 2007
"... This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage func ..."
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Cited by 1 (1 self)
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This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures sufficient conditions for global optimality. It also forms a natural basis for developing tests on the influence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirect utility function. This nonparametric efficiency measurement framework permits to differentiate mainly between portfolio efficiency and allocative efficiency. Finally, information can, in principle, be inferred about the revealed risk aversion, prudence, temperance and other higherorder risk characteristics of investors. A meanvarianceskewnesskurtosis example on a small sample of assets serves as an empirical illustration. We also compare the relative fit of a series of lower partial moment models. Keywords: shortage function, efficient frontier, Kmoment portfolios. 1
ProfitCharging Market Makers with Bounded Loss, Vanishing Bid/Ask Spreads, and Unlimited Market Depth
"... Automated market makers are algorithmic agents that price fixedodds bets with traders. Four key qualities for automated market makers have appeared in the artificial intelligence literature: (1) bounded loss, (2) the ability to make a profit, (3) a vanishing bid/ask spread, and (4) unlimited market ..."
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Cited by 1 (0 self)
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Automated market makers are algorithmic agents that price fixedodds bets with traders. Four key qualities for automated market makers have appeared in the artificial intelligence literature: (1) bounded loss, (2) the ability to make a profit, (3) a vanishing bid/ask spread, and (4) unlimited market depth. Intriguingly, market makers that satisfy any three of these desiderata have appeared in the literature. However, it is an open question as to whether there exist market makers which can simultaneously satisfy all four of these properties; the issue is not simple to resolve because several of the qualities are oppositional, particularly in tandem. In this paper, we answer the open question in the affirmative by constructing market makers that satisfy all four qualities.
THREE DISTRIBUTIONAL SHIFTS
, 2002
"... Abstract: We show that, if an individual’s utility function exhibits a degree of relative temperance smaller than one, the individual will react, in a plausible way, to each of three common shifts in the stochastic distribution of his wealth, namely to FSD shifts, meanpreserving spreads, and increa ..."
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Abstract: We show that, if an individual’s utility function exhibits a degree of relative temperance smaller than one, the individual will react, in a plausible way, to each of three common shifts in the stochastic distribution of his wealth, namely to FSD shifts, meanpreserving spreads, and increases in downside risk. First, we derive, in a unified setting, necessary and sufficient conditions for signing the comparativestatic effects of each of these shifts separately, and, second, we invoke implications of the property of mixed risk aversion to merge these separate conditions into a single sufficient condition for jointly signing all comparativestatic effects. 2 THE DEMAND FOR A RISKY ASSET:
The Distribution of Risk Aversion ∗
, 2005
"... This paper develops a framework for deriving and inferring the distribution of relative risk aversion from financial markets. The theoretical constructions (i) rely on a fairly robust form of aggregating the marginal rate of substitution of individuals that are either long or short the marketindex, ..."
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This paper develops a framework for deriving and inferring the distribution of relative risk aversion from financial markets. The theoretical constructions (i) rely on a fairly robust form of aggregating the marginal rate of substitution of individuals that are either long or short the marketindex, and (ii) specifies a positive measure for the risk aversion coefficient capturing the feature that a proportion of the population possesses a distinct risk aversion. The implementation of the theoretical model reveals substantial heterogeneity in the coefficient of relative risk aversion. Our empirical approach supports the competitive markets paradigm that enforces positive skewness in the risk aversion distribution. The evidence also points to the presence of a risk aversion distribution that is characterized by heavy tails. We discuss the asset pricing implications of theory and empirical findings.
Centre de Referència en Economia Analítica Barcelona Economics Working Paper Series Working Paper nº 9 Stochastic Dominance and Absolute Risk Aversion
"... In this paper we propose the inÞmum of the ArrowPratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave util ..."
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In this paper we propose the inÞmum of the ArrowPratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can Þnd two utility functions in this class yielding opposite preference relations for the two distributions. JEL classiÞcation codes: D81, D30.
The Impact of Prudence on Optimal Prevention Revisited ∗
, 2010
"... This paper reexamines the link between absolute prudence and selfprotection activities. We show that the level of effort chosen by an agent with positive and decreasing absolute prudence is larger than the optimal effort chosen by a riskneutral agent if the degree of absolute prudence is less tha ..."
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This paper reexamines the link between absolute prudence and selfprotection activities. We show that the level of effort chosen by an agent with positive and decreasing absolute prudence is larger than the optimal effort chosen by a riskneutral agent if the degree of absolute prudence is less than a threshold that is utilityindependent and empirically verifiable. We explain this threshold by a tradeoff between the variation of the variance and the level of the third moment of the loss distribution. We also discuss our result in terms of skewness. Our contribution extends the models of Eeckhoudt and Gollier (2005) and Chiu (2005b).
Bonn
"... ii.v meinen ElternAcknowledgements First of all I want to thank my supervisor Eva Lütkebohmert, who introduced me to conducting research by starting my dissertation with a joint project. This collaboration was always very pleasant and fruitful. I learned a lot from her deep insights into banking reg ..."
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ii.v meinen ElternAcknowledgements First of all I want to thank my supervisor Eva Lütkebohmert, who introduced me to conducting research by starting my dissertation with a joint project. This collaboration was always very pleasant and fruitful. I learned a lot from her deep insights into banking regulation as well as from her mathematical expertise. Later on she also gave me the freedom to start my own research agenda. Further, she always took her time to discuss my research as well as my plans and ambitions. I also want to thank Harris Schlesinger. My research on higherorder risk preferences has significantly benefited from numerous communications with him over the recent years. I thank Klaus Sandmann for chairing my dissertation committee and for other things (see below). I want to thank Urs Schweizer, Silke Kinzig, and their team for passionately running the Bonn Graduate School of Economics. I am very thankful to my coauthor and close friend Daniel Wiesen for the successful collaboration. It has been great fun discussing ideas, conducting experiments, analyzing data, and writing papers with him. Further, I very much have to thank Louis Eeckhoudt