Near-Optimality In Stochastic Control Of A Capital Accumulation Systems

This paper mainly studies the near-optimality in stochastic control of an capital accumulation system. Deterministic systems are often not universal, because in the system, capital accumulation is influenced by many factors, such as the innovation of technology, new product introduction, the new policy changes and so on. This makes capital become risky, which will produce irregular change, rapid change, or have no relevance in the process or the self-similarity, so put some random factors in the external environment is introduced into the model, make it more perfect and reasonable. The main research content has the following several aspects1、By constructing Hamiltonian function and adjoint equation, using Ekeland variational princi-ple、the Ito equation of Brown motion、Burkholder-Davis-Gundy inequality and some related the-ories, we research the necessary and sufficient conditions for near-optimality in stochastic control of an capital accumulation system with Brown motion.2、Considering the reality of some influence,we introduced the Poisson process into a stochastic capital accumulation system, by constructing Hamiltonian function and adjoint equation, using Ekeland variational principle、Ito equation、Burkholder-Davis-Gundy inequality and Holder inequality, we studied the necessary and sufficient conditions for near-optimality in stochastic control of an capital ac-cumulation system with Poisson jumps.3、We research a stochastic capital accumulation system with fractional Brown motion and Pois-son jumps, the fractional Brown motion have self-similarity and non-stationary, is the inscape of many phenomena, the system always with Poisson process, it is can reflect the reality of all kinds of interfer-ence, it makes research has more practical meaning. By constructing Hamiltonian function and adjoint equation, using Ekeland variational principle、the nature of the fractional Brown motion、Ito equation of fractional Brown motion and some inequality, we studied the necessary and sufficient conditions for near-optimality in stochastic control of an capital accumulation system with fractional Brown motion and Poisson jumps.