: In the study of real-valued representations (Paretian utility functions) of a completely preordered space (Space of actions preordered by preferences), the continuity properties of the representation can be made to rest on the following result. R will denote the extended real line, i.e., the real line with negative infinity and positive infinity adjoined. A degenerate set is a set having at most one element. Given a subset S of R, a lacuna of S is a non-degenerate interval of R without points of S but having a lower bound and an upper bound in S; a gap of S is a maximal lacuna of S. (Author)

On the continuity properties of paretian utility

Die Zinstheorie = the theory of interest : as determined by impatience to spend income and opportunity to invest it

Publisher Summary This chapter discusses the psychology of risk: what risk is (if it is anything at all), how people think about it, what they feel about it, and what they do about it. The chapter describes the way psychologists think about risk: how they study it, what tasks they use, what factors they vary, and what models they build (or borrow) to describe risk-taking behavior. Technically, the word risk refers to situations in which a decision is made whose consequences depend on the outcomes of future events having known probabilities. Psychological studies of risky choice (it is the term used conventionally to refer to all but the most extreme instances of ignorance or ambiguity) fall into two groups. At one extreme are the studies run by mathematically inclined experimental psychologists in which subjects make decisions about gambles described in terms of amounts and probabilities. At the other extreme are studies run by personality psychologists, who are mostly interested in individual differences in risk taking. A theory of risky choice is presented in the chapter that attempts to meld the strengths of both approaches. Empirically and methodologically it is tied to the experimental approach to risky choice. But theoretically it is more strongly tied to motivational approaches.

[Advances in Experimental Social Psychology] Advances in Experimental Social Psychology Volume 20 Volume 20 || Between Hope and Fear: The Psychology of Risk

Intertemporal decision making under risk involves two dimensions: time preferences and risk preferences. This paper focuses on the impact of time on risk preferences, independent of the intertemporal trade-off of outcomes, i.e., time preferences. It reports the results of an experimental study that examines how delayed resolution and payment of risky options influence individual choice. We used a simple experimental design based on the comparison of two-outcome monetary lotteries with the same delay. Raw data clearly reveal that subjects become more risk tolerant for delayed lotteries. Assuming a prospect theory-like model under risk, we analyze the impact of time on utility and decision weights, independent of time preferences. We show that the subjective treatment of outcomes (i.e., utility) is not significantly affected by time. In fact, the impact of time is completely absorbed by the probability weighting function. The effect of time on risk preferences was found to generate probabilistic optimism resulting in a higher risk tolerance for delayed lotteries.

Risk Preferences at Different Time Periods: An Experimental Investigation

Traditional theories in economics state that people make their decisions in order to maximize their utility function and all the relevant constraints and preferences are included and weighted appropriately In other words, in standard models, it is usually assumed that decision makers are fully rational However, some studies in behavioral economics and finance suggest that individuals deviate from standard models Behavioral economic models try to make standard models more realistic by modifying these assumptions This thesis focuses on some applications of behavioral economics in three chapters Chapter 1 focuses on individuals’ deviations from standard preferences Based on standard models, individuals have the same preferences about future plans at different points in time and the discounting factor between any two time periods is independent of when utility is evaluated However, robust laboratory experiments show choice reversal behavior in humans and animals The aim of chapter 1 is to find an approach for measuring the decision makers’ awareness of choice reversal by analyzing demand for commitment We use the data from an experimental study by Casari (2009) to measure the awareness of the selfcontrol problem Also, the welfare implications of introducing a commitment device are studied in this chapter The results show that decision makers are partially aware of their self-control problems Moreover, introducing a costless commitment device can increase the total welfare of the studied population This increase depends on individuals’ awareness of future choice reversal The aim of chapter 2 is to analyze stock price movements as a result of fundamental or technical shocks under a heterogeneous agents model (HAM) In this study, it is assumed that the market involves heterogeneous agents that have different rules for trading and that prices are endogenously determined through interactions between these agents I use the numerical simulation method to examine changes in the prices as the result of fundamental shocks The result of this chapter indicates that increasing heterogeneity in technical trading strategies could lead to more price oscillations, which is consistent with the excess volatility in stock prices The aim of chapter 3 is to predict stock price movements under a new HAM I use the HAM framework proposed in the previous chapter The value added by this chapter is estimating stock prices in a heterogeneous agent environment where chartists use different moving average trading strategies I use monthly data from S&P 500 from 1990 until 2012 and discuss the forecasting ability of the model The results of this chapter show that the presented model has a better one-step ahead, out-of-sample forecasting power compared with Boswijk et al (2007) and Chiarella et al (2012)

Behavioral economics and its applications in finance

Thesis submitted by Jinrui Pan for the Degree of Doctor of Philosophy in the University of Manchester, and entitled, ?Time and Risk Preferences: Theoretical Models and Applications? Date of submission 2014This thesis makes contributions to two important areas of behavioural economics, namely individual decision making over time and under riskFollowing the Introduction, Chapter 2 presents a new discounting function for analysing intertemporal choice Liminal discounting, the model developed here, generalises exponential discounting in a parsimonious way It allows for well-known departures, whilst maintaining its elegance and tractability It also can be seen as an extension of quasi-hyperbolic discounting to continuous time A liminal discounter has a constant rate of time preference before and after some threshold time; the liminal point A preference foundation is provided, showing that the liminal point is derived endogenously from behaviourChapter 3 proposes an axiomatic model featuring a differential treatment of attitudes towards risk and time Such distinction has been strongly suggested by experimental research when studying intertemporal choice, since the future is inherently risky In the proposed model, non-linear probability distortions are incorporated into a dynamic model with discounted utility Time is captured by a general discounting function independent of probabilities and outcomes Utility of outcomes is captured by standard vNM utility independent of time A two-parameter probability weighting function captures intertemporal probabilistic risk attitudes, with one parameter being constant over time, the other being time-dependent An index of optimism is derived that depends on both parameters, which allows to model the observed high risk tolerance for delayed lotteries Further, a preference foundation is provided Interestingly, the model allows behaviour to be consistent with discounted expected utility, when risk is sufficiently distant from the present

Jinrui Pan

Papers

Time and risk preferences : theoretical models for individual decision making