Funding, repo and credit inclusive valuation as modified option pricing

We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark vulnerable claim there is an analytical solution, and we express it in terms of the Black-Scholes formula with dividends. This allows for a detailed valuation analysis, stress testing and risk analysis via sensitivities.Comment: 1 figur

Computability, Noncomputability, and Hyperbolic Systems

In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can be computed, but (ii) globally they cannot (though we prove they are semi-computable). We also show that Smale's horseshoe, the first example of a hyperbolic invariant set which is neither an equilibrium point nor a periodic orbit, is computable

A poesia ossiânica em Portugal : estudo da sua recepção translatológica

Livro de homenagem à professora Maria Laura Bettencourt Pire

Dimensão política e de poder da comida régia e do corpo do Rei

Comer é uma necessidade natural e fisiológica de todos os homens, em todos os tempos. Mas é também uma prática cultural complexa, que convoca não só a história e a cultura material, mas também a antropologia, a sociologia, a etnologia, a psicologia, a história de arte e a história das ideias. Numa sociedade tão frágil como a dos nossos antepassados, o acto de comer era um “lugar” fundamental de diferenciação e de distinção sociais e significado político. Na verdade, a mesa do rei constituiu um instrumento político para a monarquia, desde as formas relativamente simples da Idade Média até à sua cada vez maior complexidade na Época Moderna. Neste quadro, e tomando sobretudo por base fontes históricas e documentais portuguesas dos séculos XV e XVI, este estudo analisará a mesa do rei de acordo com as seguintes perspectivas: a dimensão política e simbólica da comida régia, os alimentos que iam à mesa do monarca, o conjunto dos discursos de advertência – religioso/moralista e médico - acerca da comida régia e dos excessos cortesãos e a magnificência e ostentação dos grandes banquetes em momentos cerimoniais importantes para a monarqui

Liapunov Stability and the ring of P-adic integers

It is well-known that stable Cantor sets are topologically conjugate to adding machines. In this work we show are also conjugate to an algebraic object, the ring of P−adic integers with respect to group tramnslation. This ring is closely related to the field of p-adic numbers; connections and distintions are explored. The inverse limit construction provides a purely dynamical proof of an algebraic result: the classification of adding machines, or P−adic integers, up to group isomorphism. 

Mundializando as literaturas em português

El caso de las diversas literaturas que eligen publicar en portugués (Portugal, Brasil, Angola, Mozambique, Cabo Verde, Santo Tomé y Príncipe, junto a los casos especiales de Goa y Macao) nos permite acercarnos a la literatura mundial desde una perspectiva más compleja que la derivada de la única consideración del mundo de habla inglesa. Varios aspectos se pueden mencionar: el enriquecimiento del concepto de cosmopolitismo; la necesidad de inventar un modo de lectura que se basa en la posibilidad de alejamiento; la revisión de una idea de Europa que va más allá del eurocentrismo. La consideración de las literaturas de lengua portuguesa nos lleva a reconsiderar algunas de las bases de comparatismo y de la literatura universal.The case of the several literatures that choose to express themselves in Portuguese (Portugal, Brasil, Angola, Moçambique, Cabo Verde, São Tomé e Príncipe, next to the special cases of Goa and Macao) allows us to approach world literature from a more complex perspective than that derived from the sole consideration of the English speaking world. Several corollaries may be mentioned: the enriching of the concept of cosmopolitanism; the need to invent a way of reading that is based on the possibility of estrangement; the revision of an idea of Europe that goes beyond eurocentrism. The consideration of the Portuguese-speaking literatures leads us to reconsider some of the foundations of comparatism and of world literature.O caso das literaturas que escolhem exprimir-se maioritariamente em Português (Portugal, Brasil, Angola, Moçambique, Cabo Verde, São Tomé e Príncipe, além dos casos especiais de Goa e de Macau) permite aproximar a literatura-mundo de uma perspectiva mais complexa e enriquecedora do que a derivada do uso exclusivo do Inglês. São várias as ilações que podem ser mencionadas: o enriquecimento do conceito de cosmopolitismo; a necessidade de uma invenção da leitura que passa pela possibilidade de estranhamento; a revisão de uma ideia de Europa que não se resume a uma visão eurocêntrica. A consideração das literaturas em Português permite reequacionar alguns dos pontos de vista fundadores do comparatismo e da literatura-mundo

Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting

We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The Journal of Credit Risk, 2011). These papers state an erroneous self-financing condition. In the first paper, this is equivalent to assuming that the equity position is self-financing on its own and without including the cash position. In the second paper, this is equivalent to assuming that a subportfolio is self-financing on its own, rather than the whole portfolio. The error in the first paper is avoided when clearly distinguishing between price processes, dividend processes and gain processes. We present an outline of the derivation that yields the correct statement of the self-financing condition, clarifying the structure of the relevant funding accounts, and show that the final result in "Funding beyond discounting" is correct, even if the self-financing condition stated is not.Comment: added references, a footnote and updated abstrac

Greek and Latin historians in the Renaissance Library of D. Teodósio I, duke of Bragança

UIDB/04666/2020 UIDP/04666/2020This text has as analysis field the library of D. Teodósio I, 5th duke of Bragança, known only by a 16th century copy of his House’s inventory made after his death in 1563. As it would be expected, Antique culture is deeply represented in this great aristocratic library in all fields of knowledge – Philosophy, Poetry, Astronomy, Medicine, Theology, Civil and Canon Law. We will focus our attention on History, the most important section after Theology and Law, underlining the presence of Greek and Latin books and authors, both in their original version and in translation into vernacular languages, an eloquent testimony of the reception of Ancient Culture in Renaissance’s Portugal.publishersversionpublishe