Mathematical Programming

, Volume 134, Issue 1, pp 157–186 | Cite as

Introduction to convex optimization in financial markets

  • Teemu PennanenEmail author
Full Length Paper Series B


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

Mathematics Subject Classification

90C25 91Gxx 


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Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUK

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