Dynamic Investment Strategies to Reaction–Diffusion Systems Based upon Stochastic Differential Utilities
- 105 Downloads
We study the dynamic investment strategies in continuous-time settings based upon stochastic differential utilities of Duffie and Epstein (Econometrica 60:353–394, 1992). We assume that the asset prices follow interacting Itô-Poisson processes, which are known to be the so-called reaction–diffusion systems. Stochastic maximum principle for stochastic control problems described by some backward-stochastic differential equations that are driven by Poisson jump processes allows us to derive the optimal investment strategies as well as optimal consumption. We shall furthermore propose a numerical procedure for solving the associated nested quasi-linear partial differential equations.
KeywordsReaction–diffusion Itô-Poisson process Stochastic differential utility Stochastic maximum principle Forward-backward stochastic differential equation
Unable to display preview. Download preview PDF.
- Barles G., Buckdahn R., Pardoux E. (1997) BSDEs and integral-partial differential equations. Stochastics 60: 57–83Google Scholar
- Kashiwabara, A. (2005). Optimization of Stochastic Differential Utility Driven by Jump Diffusion Process. Working paper. Graduate School of International Corporate Strategy, Hitotsubashi University.Google Scholar
- Ma, J., & Yong, J. (1999) Forward-Backward Stochastic Differential Equations and Their Applications. Lecture Notes in Mathematics, Vol. 1702. Berlin: Springer.Google Scholar
- Shouda, T. (2005). The indifference price of defaultable bonds with unpredictable recovery and their risk premiums. Working paper. Graduate School of International Corporate Strategy, Hitotsubashi University.Google Scholar
- Yong J., Zhou X.Y. (1999) Stochastic controls: Hamiltonian systems and HJB equations. Springer, New YorkGoogle Scholar