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Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns

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  • Bruno Bouchard
  • Huy^en Pham

Abstract

We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to the usual investment in financial assets, we assume that the agents can invest part of their wealth in industrial projects that yield a nonlinear random return. We study the problem of maximizing the utility of consumption on a finite time period. The main difficulty comes from the nonlinearity of the nonfinancial assets' return. Our main result is to show that existence holds in the utility maximization problem. As an intermediary step, we prove the closedness of the set $A_T$ of attainable claims under a robust no-arbitrage property similar to the one introduced in [Schachermayer Math. Finance 14 (2004) 19--48] and further discussed in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411]. This allows us to provide a dual formulation for $A_T$.

Suggested Citation

  • Bruno Bouchard & Huy^en Pham, 2006. "Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns," Papers math/0602451, arXiv.org.
    • Handle: RePEc:arx:papers:math/0602451
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    References listed on IDEAS

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    1. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
    2. (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
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