CIR Model Under Continuous-State-Dependent Switching

Stochastic differential equation can describe a class of economic and financialphenomenon. In recent years, how to use stochastic differential equations theory toresearch the financial market has already caused more and more attention. However, asthere exist some uncertainties in financial phenomenon, which are caused by a largenumber of random factors, so it is inevitable to apply stochastic differential equation todescribe financial phenomenon. In the early1970s, the famous economist Morton andother people applied the theory of stochastic differential equation to economic theory andfinancial phenomenon and access to the remarkable results. In real financial market,short-term interest rates is one of the most fundamental and important financial number,there have been a lot of classic stochastic differential equation model describe thefinancial quantity, and the most classic of short-term interest rate model is classicCox-Ingersoll-Ross interest rate model which was mentioned by Cox, Ingersoll and Ross.This model is short for CIR model. CIR model has very important properties and gets awide range of applications，so more and more stochastic differential equation are used todescribe it, such as Markov-switching model.Due to the state–dependent switching caused more and more attention. In this article,we will put forward the CIR model under continuous-state-dependent switching. The CIRmodel under continuous-state-dependent switching is much more complex than stochasticdifferential equations without switching. In this paper we will study about the truesolution’s properties, including weak continuity, continuous and smooth dependence onthe initial data s with continuous-state-dependent switching. The numerical approximationbetween the true solution and numerical solution is also mentioned.