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On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization

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  • Di Tella, Paolo

Abstract

In this paper we show that the weak representation property of a semimartingale X with respect to a filtration F is preserved in the progressive enlargement G by a random time τ avoiding F-stopping times and such that F is immersed in G. As an application of this, we can solve an exponential utility maximization problem in the enlarged filtration G following the dynamical approach, based on suitable BSDEs, both over the fixed-time horizon [0,T], T>0, and over the random-time horizon [0,T∧τ].

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  • Di Tella, Paolo, 2020. "On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 760-784.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:760-784
    DOI: 10.1016/j.spa.2019.03.013
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    References listed on IDEAS

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    1. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    2. Jeanblanc, Monique & Song, Shiqi, 2015. "Martingale representation property in progressively enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4242-4271.
    3. Tahir Choulli & Catherine Daveloose & Mich`ele Vanmaele, 2015. "A martingale representation theorem and valuation of defaultable securities," Papers 1510.05858, arXiv.org, revised May 2018.
    4. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    5. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    6. repec:dau:papers:123456789/1803 is not listed on IDEAS
    7. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
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    Cited by:

    1. Paolo Tella, 2022. "On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2194-2216, December.
    2. Di Tella, Paolo & Jeanblanc, Monique, 2021. "Martingale representation in the enlargement of the filtration generated by a point process," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 103-121.
    3. Salmerón Garrido, José Antonio & Nunno, Giulia Di & D'Auria, Bernardo, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," DES - Working Papers. Statistics and Econometrics. WS 35411, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Jos'e A. Salmer'on & Giulia Di Nunno & Bernardo D'Auria, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," Papers 2208.07163, arXiv.org, revised May 2023.
    5. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.

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