The Study Of Optimal Investment Strategy For Pension Under Knightian Uncertainty

With the increasing scale of pensions, more and more scholars began to study the problem of optimal investment of pension. Early researchers mainly studied the investment issues of defined benefit pension. With the improvement of the pension system, the defined contribution pension plan has become the mainstream of the pension system, and some scholars began to study an optimal investment strategy for defined contribution pension plan under the complete financial market. Recently, some researchers have considered Knightian uncertainty on investment strategy, and the models of the investment strategy approaching economic realities are set up.The Knightian uncertain in this thesis is different from the traditional risk. The so-called risk refers to the uncertainty of an event occuring whose probability is known, but the Knightian uncertainty refers to the one of probability of the event occuring. It is verified that the effect of Knightian uncertainty on earnings is more significant. In order to improve the investment model, we introduce Knightian uncertainty into the model. In addition, when a company pays out dividends, the investment profit of the agent will increase, thus the agent will invest more in this company. So it is necessary to consider the factor of dividend payment in our model. As we know that the inflation also has influence on investment strategy and consumption decision, we will get a more meaningful investment model by considering of dividend payment and inflation under Knightian uncertainty, and this model can provide more effective theoretical analysis basis for an agent.This thesis study an optimal investment strategy for defined contribution pension plan with both dividend payment and inflation under Knight uncertainty. Firstly, we respectively establish an agent’s wealth dynamic equations with dividend payment and inflation under Knightian uncertainty. Secondly, we respectively characterize the agent’s expected utility functions with dividend payment and inflation by the stochastic control theory, where the agent has different levels of ambiguity aversion to different companies. Then we get two HJB equations, which are solved to obtain the explicit form solutions of the optimal investment strategy. Finally, we analyze the impacts of the ambiguity, dividend payment and inflation on the optimal investment strategy of an agent through a numerical simulation.