ABSTRACT
Operations research provides a rich set of tools and techniques that are applied to financial decision making. The first topic that likely comes to mind for most readers is Markowitz’s
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Nobel Prize-winning treatment of the problem of portfolio diversification using quadratic programming techniques. This treatment, which first appeared in 1952, underlies almost all of the subsequent research into the pricing of risk in financial markets. Linear programming, of course, has been applied in many financial planning problems, from the management of working capital to formulating a bid for the underwriting of a bond issue. Less well known is the fundamental role that duality theory plays in the pricing of options and contingent claims, both in its discrete state and time formulation using linear programming and in its continuous time counterparts. This duality leads directly to the Monte Carlo simulation method for pricing and evaluating the risk of options portfolios for investment banks; this activity probably comprises the single greatest use of computing resources in any industry.
