Study On Stochastic Control And Portfolio Problem With Jump Diffusions Market

With the rapid economical development，the flooding of information has stronglyimpacted investor’s selection on investment portfolio. But the existing investment portfoliomodel taking into significant information or emergency is more less, and that can no longermeet real needs. The jump diffusion market model is gradually considered by someresearchers. On the one hand, the model can depict the impact on asset price by every kind ofsignificant information, on the other hand, the model can reflect the practical situation morebetter. This paper will study the investment portfolio problem under this market. The mainwork and results are mainly in Chapter3,4.In Chapter3, the combined optimal stopping and stochastic control of jump diffusions isconsidered. In the first place, we consider optimal stopping model. On this basis, we buildmodel of the combined optimal stopping and stochastic control. We derive the expressions ofthe investment portfolio by utilizing the dynamic programming principle and HJB equation.Finally, we identified the reasonableness of the model by some examples.In Chapter4, the combined impulse control and stochastic control of jump diffusions isconsidered. In the first place, we consider impulse control model. On this basis, we buildmodel of the combined impulse control and stochastic control. We derive the expressions ofthe investment portfolio by utilizing the dynamic programming principle and HJB equation.Finally, we identified the reasonableness of the model by some examples.