The Distribution Of Stopping Time And State Transition Problem Of Asset Pricing

In the recent years, domestic and foreign economic has varied a lot which makesmany economic variables experience mutation sometime. In another words, the economicresearch objects also changed. So this paper mainly researches the state transition problem ofasset pricing. At the beginning, only through the numerical solution method to solve the statetransition, but this method has many limitations, not easy to find the right equation. Later,many scholars use the model of Markovian Switching to study the issue of state transitions.The most critical problem of Markovian Switching is how to determine the orders.In this paper, the distribution of stopping time is applied to the state transitions of assetpricing. Firstly we use measurement equivalence, strong markov and Girsanov theoremswhich in the random process to solve Laplasse transform,which of the stopping time of shiftBrownian motion and with indicator function of Brown motion.And by imitating the proofand the solving process of distribution of stopping time of the Brown motion, we calculate theLaplace transform of stopping time of the arithmetic Brown motion and geometric Brownmotion.In the discussion of state transition, this paper also relates to the problem that state isreversible or not. In the case of irreversible, we discuss the unilateral intervention andbilateral intervention. In the case of reversible, we study the absorbing boundary and theboundary which is not restricted. In this paper, under the different intervention policy,theaverage time before authority and the condition probability of intervention,which calculationsare given by proposition3.3, proposition3.4and proposition3.6.Finally, we discussed the asset pricing problem,which the foundation assets driven by thearithmetic Brownian motion and geometric Brownian motion. And we also give importantapplications examples. The solving process and the conclusions of the practicality andoperability are strong. In practical application, we can choose the right payment functionaccording to the actual assets.