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Optimal Investment-consumption for Partially Observed Jump-diffusions

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Seminar on Stochastic Analysis, Random Fields and Applications VII

Part of the book series: Progress in Probability ((PRPR,volume 67))

Abstract

We deal with an optimal consumption-investment problem under restricted information in a financial market where the risky asset price follows a non-Markovian geometric jump-diffusion process. We assume that agents acting in the market have access only to the information flow generated by the stock price and that their individual preferences are modeled through a power utility. We solve the problem with a two steps procedure. First, by using filtering results we reduce the partial information problem to a full information one involving only observable processes. Next, by using dynamic programming, we characterize the value process and the optimal-consumption strategy in terms of solution to a backward stochastic differential equation.

Mathematics Subject Classification (2010). Primary 91B70, 93E20, 60G35; Secondary 91B16, 60G57, 60J60.

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Author information

Authors and Affiliations

  1. Dipartimento di Economia, Università di Chieti-Pescara, I-65127, Pescara, Italy

    Claudia Ceci

Authors
  1. Claudia Ceci
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Correspondence to Claudia Ceci .

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Editors and Affiliations

  1. Institut de Mathématiques (IMA) Chaire de Statistiques Appliquées (STAP), Ecole Polytechnique Fédérale de Lausanne Fac. Sciences de Base (FSB), Lausanne, Switzerland

    Robert C. Dalang

  2. Institut Elie Cartan, Université de Lorraine, Vandoeuvre-les-Nancy CX, France

    Marco Dozzi

  3. Unité de Mathématiques appliquées, ENSTA ParisTech, Palaiseau, France

    Francesco Russo

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Ceci, C. (2013). Optimal Investment-consumption for Partially Observed Jump-diffusions. In: Dalang, R., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications VII. Progress in Probability, vol 67. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0545-2_17

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