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.
Citation
Łukasz Delong. Claudia Klüppelberg. "Optimal investment and consumption in a Black–Scholes market with Lévy-driven stochastic coefficients." Ann. Appl. Probab. 18 (3) 879 - 908, June 2008. https://doi.org/10.1214/07-AAP475
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