Optimal investment and consumption in a Black--Scholes market with Lévy-driven stochastic coefficients

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dc.creatorDelong, Łukasz
dc.creatorKlüppelberg, Claudia
dc.date2008-06-16
dc.date.accessioned2026-07-07T12:19:32Z
dc.date.available2026-07-07T12:19:32Z
dc.descriptionIn this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced with the problem of solving a nonlinear (semilinear) first-order partial integro-differential equation. A candidate solution is derived via the Feynman--Kac representation. By using the properties of an operator defined in a suitable function space, we prove uniqueness and smoothness of the solution. Optimality is verified by applying a classical verification theorem.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP475 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/0806.2570
dc.identifierhttp://arxiv.org/abs/0806.2570
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 3, 879-908
dc.identifierdoi:10.1214/07-AAP475
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212789
dc.subjectPricing of Securities
dc.subjectProbability
dc.subject93E20, 91B28 (Primary) 60H30, 60J75 (Secondary)
dc.titleOptimal investment and consumption in a Black--Scholes market with Lévy-driven stochastic coefficients
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