Work

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

Year: 2008

Type: article

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.

Source: The Annals of Applied Probability

DOI: 10.1214/07-aap475

Authors: Łukasz Delong, Claudia Klüppelberg

Institutions: SGH Warsaw School of Economics, Technical University of Munich

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: European Science Foundation

OpenAlex ID: W2032883248