Composite Prospect Theory: A proposal to combine ‘prospect theory’ and ‘cumulative prospect theory’

Evidence shows that (i) people overweight low probabilities and underweight high probabilities, but (ii) ignore events of extremely low probability and treat extremely high probability events as certain. The main alternative decision theories, rank dependent utility (RDU) and cumulative prospect theory (CP) incorporate (i) but not (ii). By contrast, prospect theory (PT) addresses (i) and (ii) by proposing an editing phase that eliminates extremely low probability events, followed by a decision phase that only makes a choice from among the remaining alternatives. However, PT allows for the choice of stochastically dominated options, even when such dominance is obvious. We propose to combine PT and CP into composite cumulative prospect theory (CCP). CCP combines the editing and decision phases of PT into one phase and does not allow for the choice of stochastically dominated options. This, we believe, provides the best available alternative among decision theories of risk at the moment. As illustrative examples, we also show that CCP allows us to resolve three paradoxes: the insurance paradox, the Becker paradox and the St. Petersburg paradox.Decision making under risk; Composite Prelec probability weighting functions; Composite cumulative prospect theory; Composite rank dependent utility theory; Insurance; St. Petersburg paradox; Becker.s paradox

Endogenous Prospect Theory.

In previous models of (cumulative) prospect theory reference-dependence of preferences is imposed beforehand and the location of the reference point is exogenously determined. This paper provides an axiomatization of a new specification of cumulative prospect theory, termed endogenous prospect theory, where reference-dependence is derived from preference conditions and a unique reference point arises endogenously.prospect theory; reference point; diminishing sensitivity; loss aversion;

Sharpening Intertemporal Prospect Theory

Prospect theory [4] of risky choices has been extended to encompass intertemporal choices [6]. Presentation of intertemporal prospect theory suffers from minor mistakes, however [2]. To clarify the theory we restate it and show further mistakes in current presentations ([6], [2]) of value and discount functions.

Priorities and prospect theory

Most would agree that priority setting is necessary to avoid a financial collapse in the health sector. It is much harder to find criteria how to do it. Discussions lead straight to the principles of decision making. But since all theories depend on assumptions given to make them work, debates on the assumption side are open for any kind of critic. This might be a reason hyprefernce-based methods for evaluations of different health states are not as common and popular as they could be. Indeed, it can be shown that results derived by such methods are severly biased by phenomenons which are summarized in a so-called Prospect Theory. These biases are quite obvious if one compares data of affected and unaffected people. But this theory offers, as well, a way to get results more accurate. -- Man ist sich weitgehend einig, dass eine Priorisierung im Gesundheitswesen notwendig ist, will man eine Finanzierungskrise verhindern. Die Kriterien dafür festzulegen, ist bedeutend schwieriger. Diskussionen kreisen immer wieder um die grundlegenden Annahmen, wie Entscheidungen getroffen werden. Da man gezwungen ist, Verhaltensaxiome festzulegen, sind darauf aufbauende, präferenz-basierte Methoden zur Evaluation von Gesundheitszuständen nicht so weit verbreitet, wie es denkbar wäre. Tatsächlich lässt sich zeigen, dass derart erzielte Ergebnisse verzerrt sind durch Phänomene, die von Kahneman und Tversky 1979 in der sogenannten Prospect Theory zusammengefasst wurden. Diese Verzerrungen werden deutlich im Vergleich von Evaluationen betroffener und nicht-betroffener Personen. Auf der anderen Seite bietet diese Theorie die Möglichkeit, Ergebnisse entsprechend zu korrigieren.

Prospect theory and hedging risks

The prospect theory is one of the most popular decision-making theories. It is based on the S-shaped utility function, unlike the von Neumann and Morgenstern (NM) theory, which is based on the concave utility function. The S-shape brings in mathematical challenges: simple extensions and generalizations of NM theory into the prospect theory cannot be frequently achieved. For example, the nature of monotonicity of the indifference curve depends on the underlying mean. Price hedging decisions also become more complex within the prospect theory. We discuss these topics in detail and offer a general result concerning the sign of a covariance from which we then infer desired properties of the indifference curve and also justify hedging decisions within the prospect theory. We illustrate our general considerations with a thoroughly worked out example. --prospect theory,mean-variance model,indifference curve,price uncertainty,hedging

Loss Aversion in Aggregate Macroeconomic Time Series

Prospect theory has been the focus of increasing attention in many Fields of economics. However, it has scarcely been addressed in macro-economic growth models - neither on theoretical nor on empirical grounds. In this paper we use prospect theory in a stochastic optimal growth model. Thereafter, the focus lies on linking the Eulerequation obtained from a prospect theory growth model of this kind to real macroeconomic data. We will use Generalized Method of Moments (GMM) estimation to test the implications of such a non-linear prospect utility Euler equation. Our results indicate that loss aversion can be traced in aggregate macroeconomic time series.Ramsey growth model, loss aversion, prospect theory, GMM

The Behavioral Economics of Crime and Punishment

The Becker proposition (BP) is one of the founding pillars of the modern literature on Law and Economics. It states that it is optimal to impose the severest possible punishment (to maintain effective deterrence) at the lowest possible probability (to economize on enforcement costs). The BP is not consistent with the evidence. This is known as the Becker paradox. Using evidence from a wide range of phenomena we show that none of the proposed explanations for the Becker paradox are satisfactory. The BP has largely been considered within an expected utility framework. We clarify the Becker proposition and its welfare implications under expected utility. We show that BP also holds under rank dependent expected utility and cumulative prospect theory, the two main alternatives to expected utility. al-Nowaihi and Dhami (2010a) recently propose composite cumulative prospect theory that combines prospect theory with cumulative prospect theory. Under plausible conditions CCP is able to resolve the Becker paradox. Our article opens the way for incorporating non-expected utility theories into an economic analysis of criminal activity.Behavioral economics; Illegal activity; Expected utility theory; Rank dependent expected utility; Prospect theory; Prelec and composite Prelec probability weighting functions; Composite cumulative prospect theory; Punishment functions

Prospect Theory and Asset Prices

We propose a new framework for pricing assets, derived in part from the traditional consumption-based approach, but which also incorporates two long-standing ideas in psychology: prospect theory, and evidence on how prior outcomes affect risky choice. Consistent with prospect theory, the investor in our model derives utility not only from consumption levels but also from changes in the value of his financial wealth. He is much more sensitive to reductions in wealth than to increases, the ``loss-aversion'' feature of prospect utility. Moreover consistent with experimental evidence, the utility he receives from gains and losses in wealth depends on his prior investment outcomes; prior gains cushion subsequent losses -- the so-called 'house-money' effect -- while prior losses intensify the pain of subsequent shortfalls. We study asset prices in the presence of agents with preferences of this type, and find that our model reproduces the high mean, volatility, and predictability of stock returns. The key to our results is that the agent's risk-aversion changes over time as a function of his investment performance. This makes prices much more volatile than underlying dividends and together with the investor's loss-aversion, leads to large equity premia. Our results obtain with reasonable values for all parameters.

Prospect Theory and Asset Prices

We study asset prices in an economy where investors derive direct utility not only from consumption but also from fluctuations in the value of their financial wealth. They are loss averse over these fluctuations and the degree of loss aversion depends on their prior investment performance. We find that our framework can help explain the high mean, excess volatility and predictability of stock returns, as well as their low correlation with consumption growth. The design of our model is influenced by prospect theory and by experimental evidence on how prior outcomes affect risky choice.

Further Reflections on Prospect Theory

This paper reports a new experimental test of prospect theoryâ??s reflection effect. We conduct a sequence of experiments that allow us to directly compare choices under reflected gains and losses where real and hypothetical payoffs range from several dollars to over $100. Lotteries with positive payoffs are transformed into lotteries over losses by reflecting all payoffs around zero. When we use hypothetical payments, more than half of the subjects who are risk averse for gains turn out to be risk seeking for losses. This "reflection effect" is diminished considerably with cash payoffs, where the modal choice pattern is to exhibit risk aversion for both gains and losses. However, we do observe a significant difference in risk attitudes between losses (where most subjects are approximately risk neutral) and gains (where most subjects are risk averse). Reflection rates are further reduced when payoffs are scaled up by a factor of 15 (for both real and hypothetical payoffs).