Zur Bestimmung des Adrenalins

Ohne Zusammenfassung     

Non-differentiable transformations preserving stochastic dominance

In this paper, we solve the following problem: when does a stochastic improvement in one risk maintain itself under a non everywhere continuously differentiable transformation of this risk? Using the notion of divided differences, we show that stochastic dominance at the third (and higher) order, and sometimes at the second one, is not preserved after simple piecewise linear transformation of the initial risk. Our analysis complements the one that exists for everywhere continuously differentiable transformations.     

Die Bestimmung des wirksamen Chlors im Chlorkalk oder in Hypochloriten wird nach 0ctave Lecomte) in einfacher Weise so

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Making inefficient market indices efficient

This paper uses the concept of Marginal Conditional Stochastic Dominance and a generalization of the 50% Portfolio Rule to develop a tractable and parsimonious methodology for constructing a second degree Stochastic Dominance (SSD) efficient portfolio from a given, inefficient index. Because the SSD approach considers the entire probability distributions of asset returns, the resulting portfolios are efficient with respect to all risk-averse, utility-maximizing investors regardless of the form of their utility functions or the distributions of asset returns.     

On the Study of Processes of $$\sum (H)$$ and $$\sum _\mathrm{s}(H)$$∑s(H) Classes

In papers by Yor, a remarkable class \(({\varSigma })\) of submartingales is introduced, which, up to technicalities, are submartingales \((X_{t})_{t\ge 0}\) whose increasing process is carried by the times t such that \(X_{t}=0\). These submartingales have several applications in stochastic analysis: for example, the resolution of Skorokhod embedding problem, the study of Brownian local times and the study of zeros of continuous martingales. The submartingales of class \(({\varSigma })\) have been extensively studied in a series of articles by Nikeghbali (part of them in collaboration with Najnudel, some others with Cheridito and Platen). On the other hand, stochastic calculus has been extended to signed measures by Ruiz de Chavez (Le théorème de Paul Lévy pour des mesures signées. Séminaire de probabilités (Strasbourg). Springer, Berlin, 1984) and Beghdadi-Sakrani (Calcul stochastique pour les mesures signées. Séminaire de probabilités (Strasbourg). Springer, Berlin, 2003). In Eyi Obiang et al. (Stochastics 86(1):70–86, 2014), the authors of the present paper have extended the notion of submartingales of class \(({\varSigma })\) to the setting of Ruiz de Chavez (1984) and Beghdadi-Sakrani (2003), giving two different classes of stochastic processes named classes \(\sum (H)\) and \(\sum _\mathrm{s}(H)\) where from tools of the theory of stochastic calculus for signed measures, the authors provide general frameworks and methods for dealing with processes of these classes. In this work, we first give some formulas of multiplicative decomposition for processes of these classes. Afterward, we shall establish some representation results allowing to recover any process of one of these classes from its final value and the last time it visited the origin.