Asia-Pacific Financial Markets

, Volume 18, Issue 2, pp 131–150 | Cite as

Dynamic Investment Strategies to Reaction–Diffusion Systems Based upon Stochastic Differential Utilities

  • Akira Kashiwabara
  • Nobuhiro Nakamura


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.


Reaction–diffusion Itô-Poisson process Stochastic differential utility Stochastic maximum principle Forward-backward stochastic differential equation 


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© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Cardif Assurance VieTokyoJapan
  2. 2.Graduate School of International Corporate StrategyHitotsubashi UniversityTokyoJapan

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