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

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dc.creatorBouchard, Bruno
dc.creatorPham, Huyên
dc.date2006-02-21
dc.date.accessioned2026-07-07T12:11:15Z
dc.date.available2026-07-07T12:11:15Z
dc.descriptionWe 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 $A_T$ 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 Rásonyi Finance and Stochastics 7 (2003) 403--411]. This allows us to provide a dual formulation for $A_T$.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000467 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0602451
dc.identifierhttp://arxiv.org/abs/math/0602451
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 4, 2393-2421
dc.identifierdoi:10.1214/105051605000000467
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210163
dc.subjectProbability
dc.subjectComputational Finance
dc.subject60G42 (Primary)
dc.titleOptimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns
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