## The Annals of Applied Probability

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

#### Abstract

We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and Rásonyi 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 AT 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 Rásonyi Finance and Stochastics 7 (2003) 403–411]. This allows us to provide a dual formulation for AT.

#### Article information

Source
Ann. Appl. Probab., Volume 15, Number 4 (2005), 2393-2421.

Dates
First available in Project Euclid: 7 December 2005

https://projecteuclid.org/euclid.aoap/1133965766

Digital Object Identifier
doi:10.1214/105051605000000467

Mathematical Reviews number (MathSciNet)
MR2187298

Zentralblatt MATH identifier
1101.60026

Subjects
Primary: 60G42: Martingales with discrete parameter

#### Citation

Bouchard, Bruno; Pham, Huyên. Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns. Ann. Appl. Probab. 15 (2005), no. 4, 2393--2421. doi:10.1214/105051605000000467. https://projecteuclid.org/euclid.aoap/1133965766

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