Evolutionary Stability of Prospect Theory Preferences

We demonstrate that in simple 2 X 2 games (cumulative) prospect theory preferences can be evolutionarily stable, i.e. a population of players with prospect theory preferences can not be invaded by more rational players. This holds also if probability weighting is applied to the probabilities of mixed strategies. We also show that in a typical game with infinitely many strategies, the "war of attrition", probability weighting is evolutionarily stable. Finally, we generalize to other notions of stability. Our results may help to explain why probability weighting is generally observed in humans, although it is not optimal in usual decision problems.prospect theory, existence of Nash equilibria, evolutionary stability

Cumulative Prospect Theory and the St.Petersburg Paradox

We find that in cumulative prospect theory (CPT) with a concave value function in gains, a lottery with finite expected value may have infinite subjective value. This problem does not occur in expected utility theory. We characterize situations in CPT where the problem can be resolved. In particular, we define a class of admissible probability distributions and admissible parameter regimes for the weighting-- and value functions. In both cases, finiteness of the subjective value can be proved. Alternatively, we suggest a new weighting function for CPT which guarantees finite subjective value for all lotteries with finite expected value, independent of the choice of the value function.

Co-monotonicity of optimal investments and the design of structured financial products

We prove that, under very weak conditions, optimal financial products on complete markets are co-monotone with the reversed state price density. Optimality is meant in the sense of the maximization of an arbitrary preference model, e.g., expected utility theory or prospect theory. The proof is based on a result from transport theory. We apply the general result to specific situations, in particular the case of a market described by the Capital Asset Pricing Model or the Black-Scholes model, where we derive a generalization of the two-fund-separation theorem and give an extension to APT factor models and structured products with several underlyings. We use our results to derive a new approach to optimization in wealth management, based on a direct optimization of the return distribution of the portfolio. In particular, we show that optimal products can (essentially) be written as monotonic functions of the market return. We provide existence and nonexistence results for optimal products in this framework. Finally we apply our results to the study of bonus certificates, show that they are not optimal, and construct a cheaper product yielding the same return distributio

Prospect Theory around the World

We present results from the first large-scale international survey on risk preferences, conducted in 45 countries. We show substantial cross-country differences in risk aversion, loss aversion and probability weighting. Moreover, risk attitudes in our sample depend not only on economic conditions, but also on cultural factors, as measured by the Hofstede dimensions Individuality and Uncertainty Avoidance. The presented data might also serve as an interesting starting point for further research in cultural economics.Risk preferences; prospect theory; cross-cultural comparison

How Time Preferences Differ: Evidence from 45 Countries

We present results from the first large-scale international survey on time discounting, conducted in 45 countries. Cross-country variation cannot simply be explained by economic variables such as interest rates or in ation. In particular, we find strong evidence for cultural differences, as measured by the Hofstede cultural dimensions. For example, high levels of Uncertainty Avoidance or Individualism are both associated with strong hyperbolic discounting. Moreover, as application of our data, we find evidence for an impact of time preferences on the capability of technological innovations in a country and on environmental protection.Time preferences; Intertemporal decision; Endogenous preference; Cross-cultural comparison

A secret erosion of the lockdown? The activity patterns of Britons in March and April 2020

Using the Apple Maps Mobility Trends Reports, the Google COVID-19 Community Mobility Reports, and data from a worldwide online survey, Marc Oliver Rieger discusses trends in activity patterns in the UK during the lockdown. Specifically, he finds that there was a significant re-increase of activities before the measures were relaxed – a trend also observed in other countries

Cumulative prospect theory and the St. Petersburg paradox

Summary.: We find that in cumulative prospect theory (CPT) with a concave value function in gains, a lottery with finite expected value may have infinite subjective value. This problem does not occur in expected utility theory. The paradox occurs in particular in the setting and the parameter regime studied by Tversky and Kahneman [15] and in subsequent works. We characterize situations in CPT where the problem can be resolved. In particular, we define a class of admissible probability distributions and admissible parameter regimes for the weighting- and value functions for which finiteness of the subjective value can be proved. Alternatively, we suggest a new weighting function for CPT which guarantees finite subjective value for all lotteries with finite expected value, independent of the choice of the value function. Some of these results have already been found independently by Blavatskyy [4] in the context of discrete lotterie

Prospect theory for continuous distributions

We extend the original form of prospect theory by Kahneman and Tversky from finite lotteries to arbitrary probability distributions, using an approximation method based on weak-⋆ convergence. The resulting formula is computationally easier than the corresponding formula for cumulative prospect theory and makes it possible to use prospect theory in future applications in economics and finance. Moreover, we suggest a method how to incorporate a crucial step of the "editing phase” into prospect theory and to remove in this way the discontinuity of the original mode

Cumulative prospect theory and the St.Petersburg paradox

We find that in cumulative prospect theory (CPT) with a concave value function in gains, a lottery with finite expected value may have infinite subjective value. This problem does not occur in expected utility theory. We characterize situations in CPT where the problem can be resolved. In particular, we define a class of admissible probability distributions and admissible parameter regimes for the weighting-- and value functions. In both cases, finiteness of the subjective value can be proved. Alternatively, we suggest a new weighting function for CPT which guarantees finite subjective value for all lotteries with finite expected value, independent of the choice of the value function

Molecular Forms of Acetylcholinesterase

Several molecular forms of acetylcholinesterase are obtained from Electrophorus or Torpedo electric organs. They have been characterized by physico-chemical methods and observed by electron microscopy. The most complex D form is made up of a globular »head« containing probably twelve subunits, or three tetrameric groups of subunits, attached to a rod like tail. Two other asymmetric forms, C and A, may be derived from it by removal of one or two tetramers from the »head«. These forms can ultimately be degraded by proteolytic digestion or sonication into tetrameric and dimeric active enzymes, G and G\u27. No striking difference in the catalytic properties of these forms could be demonstrated. An analysis of their thermal denaturation suggests · that internal breaks may exist in the polypeptide chains without being revealed ,in catalytic or sedimentation properties of the molecules. /\u27:,, H=I= values demonstrate stabilizing interactions in the more complex molecules. Analysis of subunits by SDS polyacrylamide gel electrophoresis shows that one main 90 000 subunit is progressively split into a 60 000 DFP-labelled chain together with smaller peptides jn the 30 000 range. No difference could be found between D and G subunit patterns which could ibe identified to the tail component. Comparing the molecular weight of A (one tetramer plus ta il) and G (tetramer), one finds that the mass of the tail should be in the 60 000-80 000 range. Recent micrographs suggest that it consists of three strands linked to the three tetramers in the head of D. We therefore propose a three stranded collagen like structure for the tail. We discuss the possible physiological role of the asymmetric structure o.f acetylcholinesterase and its implication with the membrane association of the enzyme. Multiple forms of acetylcholinesterase are not genetically determined i,sozymes but rather represent different states of association of the active monomern. The significance of multiple forms of acetylcholinesterase, especially in mammals, is considered