Introduction to convex optimization in financial markets

Convexity arises quite naturally in financial risk management. In riskpreferences concerning random cash-flows, convexity corresponds to thefundamental diversification principle. Convexity is a basic property alsoof budget constraints both in classical linear models as well as in morerealistic models with transaction costs and constraints. Moreover, modern securities markets are based on trading protocols that result in convextrading costs. The first part of this paper gives an introduction to certain basic concepts and principles of financial risk management in simpleoptimization terms. The second part reviews some convex optimizationtechniques used in mathematical and numerical analysis of financial optimization problems