The Closure of Spectral Data for Constant Mean Curvature Tori in S3 S ^ 3

The spectral curve correspondence for finite-type solutions of the sinh-Gordon equation describes how they arise from and give rise to hyperelliptic curves with a real structure. Constant mean curvature (CMC) 2-tori in $S ^ 3$ result when these spectral curves satisfy periodicity conditions. We prove that the spectral curves of CMC tori are dense in the space of smooth spectral curves of finite-type solutions of the sinh-Gordon equation. One consequence of this is the existence of countably many real $n$-dimensional families of CMC tori in $S ^ 3$ for each positive integer $n$.Comment: 20 page

On infinitesimal deformations of cmc surfaces of finite type in the 3-sphere

We describe infinitesimal deformations of constant mean curvature surfaces of finite type in the 3-sphere. We use Baker-Akhiezer functions to describe such deformations, as well as polynomial Killing fields and the corresponding spectral curve to distinguish between isospectral and non-isospectral deformations.Comment: 19 page

Security And Potential Level Preferences With

The security level models of Gilboa (1988) and of Jaffray (1988) as well as the security and potential level model of Cohen (1992) accomodate succesfully classical Allais paradoxa while they offer an interesting explanation for their occurrence. However, experimental data suggest a systematic violation of these models when lotteries with low probabilities of bad or good outcomes are involved. The present paper develops an axiomatic model that allows for thresholds in the perception of security and potential levels. The derived representation of preferences accommodates the observed violations of the original security and potential level models and provides a natural explanation for their occurence. Additionally, a more fundamental problem of the original models is resolved.

An Axiomatization of Linear Cumulative Prospect Theory with Applications to Portfolio Selection and Insurance Demand

The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of corresponding preferences in a cumulative prospect theory (CPT) framework. CPT is one of the most promising alternatives to expected utility theory since it incorporates loss aversion, and linear utility for money receives increasing attention since it is often concluded in empirical research, and employed in theoretical applications. Rabin (2000) emphasizes the importance of linear utility, and highlights loss aversion as an explanatory feature for the disparity of significant small-scale risk aversion and reasonable large-scale risk aversion. In a sense we derive a two-sided variant of Yaari s dual theory, i.e. nonlinear probability weights in the presence of linear utility. The first important difference is that utility may have a kink at the status quo, which allows for the exhibition of loss aversion. Also, we may have different probability weighting functions for gains than for losses. The central condition of our model is termed independence of common increments. The applications of our model to portfolio selection and insurance demand show that CPT with linear utility has more realistic implications than the dual theory since it implies only a weakened variant of plunging.

An Experimental Investigation of Alternatives to Expected Utility Using Pricing Data

Experimental research on decision making under risk has until now always employed choice data in order to evaluate the empirical performance of expected utility and the alternative non-expected utility theories. The present paper performs a similar analysis which relies on pricing data instead of choice data. Since pricing data lead in many cases to a different ordering of lotteries than choices (e.g. the preference reversal phenomenon) our analysis may have fundamental different results than preceding investigations. We elicit three different types of pricing data: willingness-to-pay, willingness-to-accept and certainty equivalents under the Becker-DeGroot-Marschak (BDM) incentive mechanism. One of our main result shows that the comparative performance of the single theories differs significantly under these three types of pricing data.experiments

Security and Potential Level Preferences with Thresholds

The security level models of Gilboa (1988) and of Jaffray (1988) as well as the security and potential level model of Cohen (1992) and Essid (1997) successfully accommodate classical Allais paradoxes while they offer an interesting explanation for their occurrence. However, experimental data suggest a systematic violation of these models when lotteries with low probabilities of bad or good outcomes are involved. In our opinion, one promising candidate for the explanation of these violations is the assumption of thresholds in the perception of security and poten- tial levels. The present paper develops an axiomatic model that allows for such thresholds, so that the derived representation of preferences can accommodate the observed violations of the original security and potential level models.Allais paradoxes, Security Level, Potential Level, Thresholds

Risk Aversion in Cumulative Prospect Theory

This paper characterizes the conditions for risk aversion in cumulative prospect theory where risk aversion is defined in the strong sense (Rothshild Stiglitz 1970). Under weaker assumptions than differentiability we show that risk aversion implies convex weighting functions for gains and for losses but not necessarily a concave utility function. Also, we investigate the exact relationship between loss aversion and risk aversion. We illustrate the analysis by considering two special cases of cumulative prospect theory and show that risk aversion and convex utility may coexist.

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;

An Experimental Investigation of the Disparity between WTA and WTP for Lotteries

In this paper we experimentally investigate the disparity between willingness-to-accept (WTA) and willingness-to-pay (WTP) for risky lotteries. The direction of the income effect is reversed by endowing subjects with the highest price of a lottery when asking the WTP question. Our results show that the income effect is too small to be the only source of the disparity. Since the disparity concentrates on a subsample of subjects, parametric and nonparametric tests of the WTA-WTP ratio may lead to contradictory results. The disparity is significantly reduced when background risk is introduced. That is, putting subjects always into a risky position could improve the contingent valuation method which is often concerned with the assessment of risky situations such as health risks, automobile safety, etc. --WTA-WTP disparity,lotteries,background risk,contingent valuation