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.
@article{1211819788,
author = {Delong, \L ukasz and Kl\"uppelberg, Claudia},
title = {Optimal investment and consumption in a Black--Scholes market with L\'evy-driven stochastic coefficients},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 879-908},
language = {en},
url = {http://dml.mathdoc.fr/item/1211819788}
}
Delong, Łukasz; Klüppelberg, Claudia. Optimal investment and consumption in a Black–Scholes market with Lévy-driven stochastic coefficients. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 879-908. http://gdmltest.u-ga.fr/item/1211819788/