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Theses

Développement, analyse et implémentation d’un modèle financier continu en temps

Abstract : SOFI is a software tool marketed by the company MGDIS. It is designed to the public institutions such local communities to set out multiyear budgets. SOFI is based on a discrete financial modeling. Consequently, the default of SOFI is using tables of type Excel. In this thesis, we build a new model with using an other paradigm. This new model is based on continuous-in-time modeling and uses the mathematical tools such convolution and integration, etc. The continuous-in-time financial model relies on measure theory. We created measures and fields and we used them in our modeling in order to show the consistency of the model. We have showed in this modeling how some aspects of functioning of loan with constant rate could be inserted in continuous-in-time model. We build a financial model with variable rate which allows model a rate of constant loan which is defined at borrowed time. We set the algebraic spending density_ in terms of the loan density_E by a mathematical operator. This operator is not always invertible. We study this inverse problem of the financial model on the space of square-integrable functions defined on a compact, and on radon measure space. We have developed two industrials libraries to implement measures and fields for the continuous-in-time financial model. We called them LemfAN (Library Embedded Finance And Numerical Analysis) and Lemf (Library Embedded Finance). The integration and the validation of these libraries in SOFI are succefully made.
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Tarik Chakkour. Développement, analyse et implémentation d’un modèle financier continu en temps. Analyse numérique [math.NA]. Université de Bretagne Sud, 2017. Français. ⟨NNT : 2017LORIS468⟩. ⟨tel-01981807⟩

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