Browsing by Author "TAHRAOUI Fatima Zohra"

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    Problème de consommation optimale avec investissement
    (2018-05-15) TAHRAOUI Fatima Zohra; Encadreur: LIMAM-BELARBI Faiza
    Résumé (Français et/ou Anglais) : - One of the principal questions in mathematical finance is the optimal investment consumption problem for continuous time market models. By applying results from stochastic control theory, explicit solutions have been obtained for some special cases (see e.g. Karatzas and Shreve 1998, Korn 1997and references therein). Kluppelberg and Pergamenshchikov 2010 considered the optimal investment/consumption problem with uniform risk limits throughout the investment horizon for power utility functions. - In this thesis, we investigate an optimal consumption and investment problem for Black-Scholes type financial market on the whole investment interval [0, T]. We formulate various utility maximization problems, which can be solved explicitly. The method of solution uses the convex dual function (Legendre transform) of the utility function. Related to this concept, we introduce and study the convex dual of the value function for our problem.