The Central Bank's Exchange Rate Intervention Based On Pulse Control In The Inflation Environment

As is known to all,exchange rate plays a key role in global economy and trade,and the fluctuation of exchange rate has always been a key concern of a country in its import and export trade.Generally speaking,a higher exchange rate promotes imports and restricts exports;A lower exchange rate promotes exports and restricts imports,so it is important for a country to keep its exchange rate within a reasonable range.Usually a country's central bank is responsible for the country's exchange rate stability,face volatility in the exchange rate at the central bank monetary policy and fiscal policy active intervention on exchange rates,best study the central bank exchange rate intervention strategies for this problem,namely,when to currency intervention and the amplitude of the interference problem has practical significance.At the same time,due to the influence of unilateralism,trade protectionism and other measures in real economic activities,the exchange rate strategy formulation of the central bank is more complex,and since the world's economies are facing inflation,it is more realistic to consider the inflation factor when studying the central bank's exchange rate intervention.To sum up,this paper studies the modeling of the optimal intervention strategy of the central bank under the inflation environment,and gives the corresponding economic explanation by means of numerical simulation given relevant data.The main work of this paper is to study the central bank's exchange rate intervention based on the pulse control method in the inflation environment,which consists of the following five parts:The first part is the introduction.First of all,it introduces the research background and significance of this paper;then it briefly combs the research status of related content at home and abroad;finally,it mainly introduces the research content and the structure of the paper.In the second part,we study the impact of inflation fluctuation on the optimal exchange rate intervention of the central bank based on the impulse control theory.Firstly,in the inflation environment,a pulse control model of exchange rate is established.Through stochastic analysis,the quasi variational inequality satisfied by the value function of the pulse control is derived.By solving the quasi variational inequality,we can deduce the optimal exchange rate intervention strategy of the central bank.Finally,given the parameters of the model,the numerical simulation and the corresponding economic explanation are carried out.In the third part,on the basis of the second part,the jump diffusion process is added to the exchange rate model,which mainly considers the influence of Poisson jump in the exchange rate market on the central bank's exchange rate intervention strategy.By adding the jump diffusion process to the exchange rate model and through random analysis,the quasi integral variational inequality satisfied by the value function of pulse control is derived,and the quasi integral variational inequality is deduced by solving the quasi integral variational inequality.At the same time,the approximate solution of impulse control model with random response period is proposed.By solving a series of optimal stop time problems,the optimal solution of impulse control model can be obtained,which improves the applicability of the existing impulse control model framework.Finally,the numerical simulation of the results is carried out.The fourth part studies the existence and uniqueness of the optimal central bank's exchange rate intervention strategy in the inflation environment based on the third part.Firstly,in the inflation environment,a exchange rate pulse control model is established.Through random analysis,the quasi product variational inequality satisfied by the value function of the pulse control is derived.Secondly,it is proved that the optimal central bank's exchange rate intervention strategy is a control strategy.It also proves the existence and uniqueness of the optimal central bank's exchange rate intervention strategy.In the last part,the research of this paper is summarized and prospected.In the summary,the shortcomings of this paper and the further development in the future are given.