On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization |
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Affiliation: | 1. Department of Economics, University “G. D’Annunzio” of Chieti-Pescara, Viale Pindaro, 42, I-65127 Pescara, Italy;2. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123 Perugia, Italy;1. Mathematical Sciences Center and Tsinghua Center for Statistics Science, Tsinghua University, Beijing 100084, China;2. School of Economics and Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, Xiamen 361005, China;3. School of Business, Renmin University of China, Beijing 100084, China;1. CIMFAV, Facultad de Ingeniería, Universidad de Valparaíso, Casilla 123-V, 4059 Valparaiso, Chile;2. Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d’Ascq, France;3. ISMMA, Romanian Academy, Bucharest, Romania;1. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Catalonia, Spain |
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Abstract: | In this paper we show that the weak representation property of a semimartingale with respect to a filtration is preserved in the progressive enlargement by a random time avoiding -stopping times and such that is immersed in . As an application of this, we can solve an exponential utility maximization problem in the enlarged filtration following the dynamical approach, based on suitable BSDEs, both over the fixed-time horizon , , and over the random-time horizon . |
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Keywords: | Weak representation property Semimartingales Progressive enlargement of filtrations Exponential utility maximization |
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