Optimal investment and consumption in a Black--Scholes market with L\'evy-driven stochastic coefficients

{\L}ukasz Delong and Claudia Kl\"uppelberg

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Abstract: In 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.

Date: 2008-06
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Citations: View citations in EconPapers (19)

Published in Annals of Applied Probability 2008, Vol. 18, No. 3, 879-908

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