Title :
Robust maximization of consumption with logarithmic utility
Author :
Hernández-Hernández, Daniel ; Schied, Alexander
Author_Institution :
Fac. of Centro de Investigation en Matematicas, Guanajuato
Abstract :
We analyze the stochastic control approach to the dynamic maximization of the robust utility of consumption and investment. The robust utility functionals are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an external stochastic factor process. Our main results give conditions on the minimal penalty function of the robust utility functional under which the value function of our problem can be identified with the unique classical solution of a quasilinear PDE within a class of functions satisfying certain growth conditions.
Keywords :
economics; optimisation; partial differential equations; stochastic systems; external stochastic factor process; logarithmic utility; minimal penalty function; partial differential equations; robust maximization; stochastic control approach; Cities and towns; Diffusion processes; Finance; Investments; Mathematics; Q measurement; Robust control; Robustness; Stochastic processes; Utility theory;
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2007.4283154