Quantitative Finance is is a very important application of Finance because the mathematical finance is the most important aspect of the financial evaluation.As we know that in finance, the quantitative analysis is the use of the financial mathematics.This is often done with the help of the physical and statistical applications in order to perform financial analysis. Similarly, this analysis takes place in the most modern industries, although in many cases this analysis is not known in these sectors as quantitative analysis. In the investment industry, analysts who develop quantitative analysis are usually called quanta.

Although the common area of analysis of such techniques was originally the Asset Management, the risk management and pricing of the financial derivatives, the meaning of the term has expanded over time to include those individuals engaged in almost any application of mathematics in finance. Examples include the statistical arbitrage, the algorithmic trading and conducting electronic transactions in the markets.

**Mathematical and Statistical Approaches to Finance**

Quantitative analysis is often based on three types of mathematics: statistics and probability calculation focused on partial differential equations.Most quantitative analysts have little background in economics, and usually apply a set of tools from physics. Physicists usually have less experience in statistical techniques, which are often based on estimates based on partial differential equations and their solutions are often based on the numerical analysis.

The most widely used numerical methods are:

**Finite Difference Method**: It is used to solve partial differential equations, and**The Monte Carlo Method**: It is also used to solve partial differential equations, but being also common the use of Monte Carlo simulation in risk management.

**IS QUANTITATIVE FINANCE FLAWLESS?**

There has also been the criticism of the quantitative finance. The main reason for the criticism is the financial crisis in the time span of 3 years( between 2007 and 2010).It is argued that the quantitative finance was an utter failure during that crisis as it failed to provide a concrete solution.The critics argue that the financial engineering (a branch of Finance) bore fruit during that crisis.

There is also a decreasing trend of reliance on the quantitative finance because the distribution of the finance variables is also considered imperfect.Let’s take an example from the engineering finance which provides Gaussian Distribution.This distribution is the most perfect from all respects as compared to the quantitative Finance.However, with the passage of time there have been many changes in the applications of finance.A number of alternatives to the quantitative finance have emerged and some of them are standard deviation and the stable distribution.