Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2008-06-16
Annals of Applied Probability 2008, Vol. 18, No. 3, 879-908
Economy
Quantitative Finance
Pricing of Securities
Published in at http://dx.doi.org/10.1214/07-AAP475 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/07-AAP475
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.
Delong Łukasz
Klüppelberg Claudia
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