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Probabilistic methods for semilinear partial differential equations. Applications to finance

Dan Crisan, Konstantinos Manolarakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

With the pioneering work of [Pardoux and Peng, Syst. Contr. Lett.14 (1990) 55–61; Pardoux and Peng, Lecture Notes in Control and Information Sciences176 (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called backward stochastic differential equations. These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance....

Probabilistic properties of the continuous double auction

Martin Šmíd (2012)

Kybernetika

In this paper we formulate a general model of the continuous double auction. We (recursively) describe the distribution of the model. As a useful by-product, we give a (recursive) analytic description of the distribution of the process of the best quotes (bid and ask).

Problemas finitos de decisión con conocimiento cualitativo de la distribución a priori.

José A. Cristóbal (1983)

Trabajos de Estadística e Investigación Operativa

En lo que sigue, abordaremos problemas de decisión en ambiente de riesgo y con experimentación, en donde la distribución de probabilidad a priori sobre los estados de la Naturaleza no es perfectamente conocida, sino que solamente se posee una información cualitativa de la misma. Más concretamente, dados dos estados de la Naturaleza cualesquiera, se conoce a lo más, cuál de ellos es más probable que el otro, si bien no se tiene una idea cuantitativa de esta diferencia de probabilidades.

Problems with classical models of sex-ratio evolution

Krzysztof Argasiński (2008)

Banach Center Publications

The classical theory of the sex-ratio evolution, known as the sex-ratio game, is based on the maximization of the number of grandchildren, treated as a fitness measure of a female producing offspring of the sex ratio that is coded in her genes. The theory predicts that it is more profitable to produce offspring with less numerous sex. We can find in the literature mutually exclusive conclusions based on this prediction: some textbooks say that populations with the equal number of sons and daughters...

Producing the tangency portfolio as a corner portfolio

Reza Keykhaei, Mohamad-Taghi Jahandideh (2013)

RAIRO - Operations Research - Recherche Opérationnelle

One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolio selection problem for a set of some risky assets and a riskless asset can be represented by a combination of a unique risky fund (tangency portfolio) and the riskless asset. In this paper, we introduce a method for which the tangency portfolio can be produced as a corner portfolio. So, the tangency portfolio can be computed easily and fast by any algorithm designed for tracing out the M-V efficient frontier via...

Production games, core deficit, duality and shadow prices

Sjur Didrik Flåm (2006)

Banach Center Publications

Considered here are production (or market) games with transferable utility. Prime objects are explicitly computable core solutions, or somewhat "deficit" versions of such, fully defined by shadow prices. Main arguments revolve around standard Lagrangian duality. A chief concern is to relax, or avoid, the commonplace assumption that all preferences and production possibilities be convex. Doing so, novel results are obtained about non-emptiness of the core, and about specific imputations therein.

Propriétés et caractérisations topologiques d'une représentation pyramidale

P. Bertrand (1992)

Mathématiques et Sciences Humaines

Ce texte présente quelques caractéristiques géométriques des dissimilarités robinsoniennes. Ces dissimilarités constituent un modèle très général de représentation des mesures de proximité entre objets (ou groupes d'objets) lorsque ces entités sont rangées suivant un ordre total. Les propriétés géométriques des dissimilarités robinsoniennes sont exposées en utilisant les notions de segment et de frontière introduites pour une dissimilarité quelconque. Nous considérons ensuite l'ensemble des dissimilarités...

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