Near-Optimality in Stochastic Control of an Capital Accumulation System with Markovian Switching and Poisson Jumps

We introduce a class of stochastic capital system with Marvokian switching and Poisson jumps, establish necessary condition for near-optimality. The proof of the main results is based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.