Mathematical programming and its application in finance

This article reviews some of the applications of mathematical programming infinance. Of course mathematical programming has long been recognised as a vitalmodelling approach to solve optimization problems in finance. Markowitz’s NobelPrize winning work on portfolio optimization showed how important a techniqueit is. Other prominent and well documented applications in long-term financialplanning and portfolio problems include asset-liability management for pensionplans and insurance companies, integrated risk management for intermediaries,and long-term planning for individuals. Nowadays there is an emphasis on theinteraction between optimization and simulation techniques in these problemsThere are though many uses of mathematical programming in finance whichare not purely about optimizing the return on a portfolio and we will also discussthese applications. For example we discuss how one can use linear programmingto estimate the term structure of interest rates for the prices of bonds. In thepersonal sector finance, where the lending is far greater than the higher profilecorporate sector, the use of linear programming as a way of developing creditscorecards is proving extremely valuable.