JRIAM

Financial institutions are increasingly using mathematical models to help manage large portfolios of financial instruments of growing complexity. The solution of such mathematical models involves the full gamut of numerical methodologies but computational optimization plays a paramount role. In this talk we survey some of the basic computational problems of finance – option pricing and hedging, portfolio rebalancing, optimal value-at-risk (VaR and CVaR) determinations, volatility computations, and risk management of derivative portfolios – and the use of both standard and innovative optimization approaches. One surprising example, in the optimal VaR setting, illustrates that a standard LP solution can be prohibitively expensive but a nonlinear view can yield an effective and much faster solution procedure. Numerical results and illustrative examples will be sprinkled throughout the presentation.