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Simple strategies in exponential utility maximization

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Simple strategies in exponential utility maximization SÉMINAIRE DE PROBABILITÉS (STRASBOURG) CHRISTOPHE STRICKER Simple strategies in exponential utility maximization Séminaire de probabilités (Strasbourg), tome 36 (2002), p. 415-418. <http://www.numdam.org/item?id=SPS_2002__36__415_0> © Springer-Verlag, Berlin Heidelberg New York, 2002, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://www-irma. u-strasbg.fr/irma/semproba/index.shtml), implique l’accord avec les conditions gé- nérales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Simple strategies in exponential utility maximization Christophe Stricker UMR 6623, Laboratoire de Mathématiques, Université de Franche-Comté 16 Route de Gray, F-25030 Besançon Cedex, FRANCE Abstract This short note contains a ramification of one of the main results of [3] and answers a question formulated by Michel Emery. Assuming that the price process is locally bounded and admits an equivalent local martingale measure with finite entropy, we show that in the case of exponential utility the optimal value can always be attained on a sequence of uniformly bounded portfolios with simple bounded integrands. Key words: exponential utility, semimartingale topology, stochastic integrals Mathematics Subject Classification 2000: 60G42 1. . Approximating stochastic integrals. We are given a probability space (Sl, .~, P), a fixed time horizon T E (0, +oo) and a filtration satisfying the usual conditions of right continuity and com- pleteness. All our processes are defined on [0, T]. We fix throughout the paper an IRd-valued semimartingale S = (St)O::;t:5T and think of this as the discounted prices

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