Girsanov Theorem Of It(?) Process With Degenerate Coefficients And Its Applications In Finance

In this article, an expression of Girsanov theorem is given to facilitate the use.Then, by using the new theorem, we get a criterion for no arbitrage opportunitiesin a fnancial markets, which is more convenient than ever before.As is well known, Girsanov theorem is the basic theory of stochastic analysis,which has has its important applications in many ways. By focusing on the study ofGirsanov II theorem in this paper, we found that the limitations of the applicationsof the theorem. The stochastic process in the theorem is a Ito process under thecondition of Rn, which satisfy a stochastic diferential equation. However, whenthe coefcient matrix of the equation is a singular matrix, then the theorem is notsuitable for the use of. Here, by promoting Moore-Penrose generalized inverse of adegenerate coefcient matrix, get the new form of Girsanov II theorem. To applythe result in the fnancial markets, a new criterion for no arbitrage opportunities ina fnancial markets is given, which is convenient in applications.Finally, we got the results with stronger practicability. Since then, the GirsanovII theorem can be applied in wider scope. At the same time, we got the results areapplicable in the study of fnancial markets, has certain theoretical value.