Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns
Bouchard, Bruno; Pham, Huyen (2005), Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns, The Annals of Applied Probability, 15, 4, p. 2393-2421. http://dx.doi.org/10.1214/105051605000000467
TypeArticle accepté pour publication ou publié
Journal nameThe Annals of Applied Probability
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Abstract (EN)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.
Subjects / KeywordsFinancial markets with transaction costs; nonlinear returns; multivariate nonsmooth utility maximization; super-hedging theorem; robust no-arbitrage
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