Financial Engineering refers to the collective study of finance,finance theory, methods of engineering, tools of mathematics and the practice of programming as well. It is also known as mathematical finance or Financial mathematics.
It is based upon mathematics, computer science, statistics and economics.
Areas where financial engineers are hired are commercial banks, hedge funds, insurance companies, corporate treasuries and investment banks.
Financial engineering is used to address current financial issues as well as to devise new and innovative financial products and can be also termed as quantitative analysis.
Very few colleges in India offer this course out of which Institute of Mathematics and Applications , Bhubaneshwar would be one of them.
All the best.