Financial Optimization

Abstract

Many financial decision problems are most naturally formulated as optimization problems. This is the case, for example, in (arbitrage, utility, risk measure,...) pricing and hedging of (European, American, real,..) options, portfolio optimization and asset liability management. The optimization approach becomes even more natural in the presence of market imperfections such as transaction costs or portfolio constraints, where more traditional approaches of mathematical finance fail. Common to many financial problems, when properly formulated, is convexity with respect to the decision variables. This opens up possibilities of using numerical techniques that have been developed for large scale optimization problems.