In this paper primarily I focus on the application of mathematics in financial Challenges which arise in financial market. At first it is very essential to prepare a specific framework covering all aspects of applying those techniques to understand mathematical operation research on the financial market. In the beginning, this Paper discusses the attractiveness and application of operation research in the financial market.This paper also presents the frequency and the percentage of the use in financial market of various operational strategies, which analyses the proportion of the service within certain operational principles. The paper also highlights different challenges and how mathematics has applied to solve them: economic understanding, strategic difficulties, financial marketing imperfections.