Study On The Dynamical Models Of Decision Making And Regulation Problems In Financial Market With The Impulsive Effect

With the impact of the global economic situation at home and abroad, more and morescholars have committed to the study of practical problems in the field of economics,management, financial engineering and so on, which are beneficial to the people’s livelihood.Especially, affected by new international environment as well as the sluggish domesticdemand, problems about commodity pricing decision and monetary policy in moderneconomic and financial market are highly vulnerable to many external factors, such as,financial volatility, inventory of goods, capital flow, etc. Such irrational pricing and the lag ofmonetary policy would bring certain influences to the health and stable development offinancial market. Therefore, how to select an appropriate mathematical model to describe thecomplex dynamic process has been a hot issue in the field of sociology, politics, economicsand management. Atucally, as a special kind of discontinuous system, impulsive dynamicalsystem describes such complex phenomenon consisting of both continuous and discrete states,which can characterize the instantaneous external impact precisely. Hence, based on therelated research and analysis, we set up more appropriate mathematical dynamic model forthe pricing and monetary policy problems, respectively, under the influence of financialvolatility. Not only the dynamic property but also the effects of external fluctuations areconsidered.In addtion, the above two kinds of economic and financial market models can both beclassified as a class of second-order impulsive differential system, which has been widelyused in the area of biology, medicine, financel, control, physics and engineering. Thecombination of impulse and second-order differential system makes more practicalsignificances, and has become a focus in the research of dynamics. Nowadays, the studyabout the properties of complexity and stability of the equilibrium as well as attractors of theimpulsive differential system has caused the attention of many scholars.Based on the flow theory and discrete mapping dynamics, this paper utilize the method ofthe generalized harmonic balance and various metric functions to investigate on thesecond-order impulsive differential system. Some analyses on theories of complex behaviorsas well as periodic motions are obtained. Moreover, criteria about the qualitative analysis ofthe equilibrium and attractors are presented. Finally, we apply our results to practical problems, portraying the nature of pricing decision and monetary policy problems. Ourinvestigation not only provides a new method and effective theory for impulsive dynamicalsystem, but also promotes the healthy and stable development of the economic and financialmarkets, due to its reasonable modeling including appropriate response to the financialfluctuations, even the financial crisis.The full text is divided into seven chapters.In the first chapter, we first reviewed the global and domestic environment of economicsituation for commodity market in recent years. Then we discussed two kinds of specificproblems for commodity pricing and monetary policy in financial market, respectively,indicating corresponding background and application requirements of the research. From theperspective of its theoretical significance, relative research and the trend of relevant researchwere given. Besides, the main work and innovation characteristics were followedsubsequently.In the second chapter, we first summarized several established pricing models incommodity market theory, and then introduced the problem of optimal pricing decision infinancial markets, especially the influence of international commodity prices andcompetitions on the pricing of commodities. Moreover, we investigated the pricing problemof commercials when there had been instantaneous impact phenomena, causing by thefluctuations of financial market shocks, the Internet transactions, mutation of the amount ofinventory, changing of the price level and so on. And finally, a kind of nonlinear dynamicalmodel for the pricing decision problems in commodity market was established with theimpulsive effect.In the third chapter, firstly, the monetary regulation theory and the currency requirementmodel in the financial market were introduced. Then, by analyzing various practical factorswith fluctuations in the financial market, such as, the effect of mutation of the capital flow, theInternet financial shocks, the swings of the price level and the stock market, the change ofinflation and so on, we set up a kind of nonlinear dynamical model for the currency regulationand the monetary policy in financial market with the effect of impulse.In the fourth chapter, as the given two types of economic and financial market models canboth be classified as a kind of second-order impulsive differential system, we firstlyinvestigated its dynamical characteristics form the discontinuous point of view. For its phasespace, we divided it into several sub-domains and correspongding time-varying boundaries.So that, the original system could be regarded as a global discontinuous one consisting of a family of continuous sub-systems and each switching laws or impulse functions betweenadjacent domains. Utilizing the method of flow theory and various metric functions about theboundaries, we analyzed the complex behavior of the motion, especially its collision casenamed pulse phenomena in differential systems. And finally, criteria about the qualitativeanalysis of the periodic motion and equilibrium are presented..In the fifth chapter, corresponding to the pricing decision dynamical model in commoditymarket presented in Chapter Two, we applied relative theorical analysis to the practicalproblem. By means of discrete mapping structure and mapping dynamics, the nonlinearperiodic fluctuation phenomena of pricing model were disscussed, in addition, several resultsabout the existence and stability of periodic behaviors were obtained, which were bentifit tofurther knowleges of the fluctuation of pricing problems.In the sixth chapter, based on the given monetary regulation dynamical model in ChapterThree, we firstly researched on its equivalent form as a special kind of switching dynamicalsystem by specific periodic monetary policies regulation approach. By applying thegeneralized harmonic balance and discontinuous dynamical theories, further qualitativeanalysis of equilibrium was presented using different metric functions, under correspondingconceptions of stability.The seventh chapter concluded the main work of this paper, and prospected the furtherresearch of impulsive differential systems.