Nonparametric predictive utility inference

We consider the natural combination of two strands of recent statistical research, i.e., that of decision making with uncertain utility and that of Nonparametric Predictive Inference (NPI). In doing so we present the idea of Nonparametric Predictive Utility Inference (NPUI), which is suggested as a possible strategy for the problem of utility induction in cases of extremely vague prior information. An example of the use of NPUI within a motivating sequential decision problem is also considered for two extreme selection criteria, i.e., a rule that is based on an attitude of extreme pessimism and a rule that is based on an attitude of extreme optimism.     

Molp with an interactive assessment of a piecewise linear utility function

The paper presents a methodology for Multi-Objective Linear Programming (MOLP) problems. It relies on three steps: (1) Generation of a subset of feasible efficient solutions (from 10 to 50) as representative as possible of the efficient set. (2) Assessment of an additive utility function using an interactive method (Prefcalc). (3) Optimization of the additive utility function on the original set of feasible alternatives. Following this methodology enables the user to find compromise solutions which can be different from the vertices. It is particularly adapted for large scale linear programs where traditional multiobjective methods would be too costly to use, since the interactive phase is limited to step 2, using Prefcalc on a micro-computer. A micro-computer version of the method (Prefchat) is available.     

Foundations of lexicographic utility

This paper presents an alternative mathematical characterization of lexicographic utility to the one given by Chipman (1960). A natural constructivistic procedure on imposing a lexicographic ordering on the product space of natural numbers is pursued. The consequences on the topological structure of such a space are examined.     

Eigenvalue equations in curve theory

We characterize conic sections in the Euclidean plane in terms of appropriate eigenfunctions of second order on their spherical image; we clarify the affine background of such results.     

Distance in the curve graph

We estimate the distance in the curve graph of a surface $S$ of finite type up to a fixed multiplicative constant using Teichmüller geodesics.     

Sensitivity of decisions with imprecise utility trade-off parameters using boundary linear utility

In earlier work we have developed methods for analysing decision problems based on multi-attribute utility hierarchies, structured by mutual utility independence, which are not precisely specified due to unwillingness or inability of an individual or group to agree on precise values for the trade-offs between the various attributes. Our analysis is based on whatever limited collection of preferences we may assert between attribute collections. In this paper we introduce three methods to assess the robustness of our selected decision. Two of these use the metric generated by the weights of the boundary linear utility. The third applies directly to the space of trade-off parameters.     

Stability of probability effects in utility elicitation

The present study investigates the impact of probability levels on the response mode bias in utility elicitation and its stability across a wide range of conditions. Experiments are performed with subjects from two different cultures, Austria and Pakistan, and a variety of methods to measure risk attitudes of subjects on a cardinal scale are used. Results indicate robust influences of probability levels on both the Certainty Equivalent method and the Probability Equivalent method of utility elicitation. Both methods are affected by probability changes in the opposite direction, creating the characteristic “tailwhip” pattern observed in previous research. Our study shows that this effect remains stable across different cultural backgrounds, measurement methods, and problem parameters, and is thus not an artefact but a reproducible phenomenon.     

Duality in non-additive expected utility theory

Some duality problems in expected utility theory, raised by the introduction of non-additive probabilities, are examined. These problems do not arise if the probability measure is symmetric; i.e. has the property of complementary additivity. Additional, mild properties of coherence of conditional probabilities imply full additivity of the unconditional measure.     

Applications of fuzzy sets in curve fitting

This paper presents several methods for functional approximation with variable-knot variable-degree splines, with variable-knot first order splines, which are relatively easy to find, as the intermediate input. By means of a fuzzy characteristic function determining how “sharp” the angle at each knot is (the higher the polynomial degree, the “sharper” its first order spline approximation bends), we can decide whether we can group certain adjacent segments together to be approximated by a single higher order polynomial segment. Some simulation experiments have also been done.     

Neutral curve behaviour in Taylor-Dean flow

Summary Numerical investigations reveal a class of neutral curve in infinite Taylor-Dean flow not previously observed. Based on the work of Hall, asymptotic expansions at the high-wavenumber end of the neutral curves are given.Previously, an interpretation had been given by Raney and Chang for the curves observed by Hughes and Reid. Using the above expansions and Rayleigh's criterion, an alternate explanation is proposed in this paper which takes into account the new phenomena.

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Résumé Des investigations numériques ont révélé un genre de courbe de stabilité neutre dans l'écoulement infini de Taylor-Dean non observé auparavant. Basé sur l'oeuvre de Hall, des développments asymptotiques à l'extrémité de ces courbes où le nombre d'ondes est élevé sont soumis. Auparavant, des courbes ont été observées par Hughes et Reid et une interprétation a été donné par Raney et Chang. Dans ce papier, on emploie les développements susmentionés et le criterium de Rayleigh pour proposer une autre explication qui fait état de nouveau phénomène.

     

Residuals in the growth curve model

Residuals for the Growth Curve model will be discussed. In univariate linear models as well as the ordinary multivariate analysis of variance model residuals are based on the difference between the observations and the mean whereas for the Growth Curve model we have three different residuals all showing various aspects useful for validating analysis. For these residuals some basic properties are established.     

Tight geodesics in the curve complex

The curve graph, , associated to a compact surface Σ is the 1-skeleton of the curve complex defined by Harvey. Masur and Minsky showed that this graph is hyperbolic and defined the notion of a tight geodesic therein. We prove some finiteness results for such geodesics. For example, we show that a slice of the union of tight geodesics between any pair of points has cardinality bounded purely in terms of the topological type of Σ. We deduce some consequences for the action of the mapping class group on . In particular, we show that it satisfies an acylindricity condition, and that the stable lengths of pseudoanosov elements are rational with bounded denominator. Mathematics Subject Classification (2000) 20F32     

Revisiting the problem of integrability in utility theory

We revisit the problem of integrability in the consumer theory, focusing on the main difficulties. First, we look for a neat and simple local existence result, and then for a global solution. Second, observing that a utility function (or indirect utility function) cannot be determined uniquely, we propose a means to get a kind of uniqueness result. Our approach is coordinate-free and can be used both in the classical case of a finite-dimensional commodity space and in the case an infinite-dimensional model is adopted.     

Conjugate duality in problems of constrained utility maximization

We show that a simple and elegant method of Bismut [J. Math. Analysis Appl., 44 (1973), pp. 384–404] for applying conjugate duality to convex problems of Bolza adapts directly to problems of utility maximization with portfolio constraints in mathematical finance. This gives a straightforward construction of an associated dual problem together with Euler–Lagrange and transversality relations, which are then used to establish existence of optimal portfolios in terms of solutions of the dual problem. The approach is completely synthetic, and does not require the rather difficult a priori hypothesis of a fictitious complete market for unconstrained optimization, which has been the standard approach for synthesizing optimal portfolios in problems of utility maximization with trading constraints. It also complements a duality synthesis of Rogers [Lecture Notes in Mathematics, No. LNM-1814, Springer-Verlag, New York, 2003, pp. 95–131] and Klein and Rogers [Math. Finance, 17 (2007), pp. 225–247] for general problems of utility maximization with market imperfections.     

On expected utility in optimal stopping of diffusions

Suppose an agent with a static risk preference faces prize processes given by diffusion processes and decides when to stop. We show that the agent satisfies dynamic consistency of preferences if and only if she adheres to Expected Utility. This extends the classical dynamic characterization of Expected Utility to a setup of processes with continuous paths, in which the classical discrete-time proof techniques do not apply.     

A maximal curve which is not a Galois subcover of the Hermitian curve

We present a maximal curve of genus 24 defined over with q = 27, that is not a Galois subcover of the Hermitian curve. *The author was partially supported by CNPq-Brazil (470193/03-4) and by PRONEX (CNPq-FAPERJ).     

Characterization of the Fermat curve as the most symmetric nonsingular algebraic plane curve

A projective nonsingular plane algebraic curve of degree \(d\ge 4\) is called maximally symmetric if it attains the maximum order of the automorphism groups for complex nonsingular plane algebraic curves of degree \(d\) . For \(d\le 7\) , all such curves are known. Up to projectivities, they are the Fermat curve for \(d=5,7\) ; see Kaneta et al. (RIMS Kokyuroku 1109:182–191, 1999) and Kaneta et al. (Geom. Dedic. 85:317–334, 2001), the Klein quartic for \(d=4\) , see Hartshorne (Algebraic Geometry. Springer, New York, 1977), and the Wiman sextic for \(d=6\) ; see Doi et al. (Osaka J. Math. 37:667–687, 2000). In this paper we work on projective plane curves defined over an algebraically closed field of characteristic zero, and we extend this result to every \(d\ge 8\) showing that the Fermat curve is the unique maximally symmetric nonsingular curve of degree \(d\) with \(d\ge 8\) , up to projectivity. For \(d=11,13,17,19\) , this characterization of the Fermat curve has already been obtained; see Kaneta et al. (Geom. Dedic. 85:317–334, 2001).