Introduction to convex optimization in financial markets

• 成果类型: Article
• 署名作者: Pennanen, Teemu
• 署名单位: University of London; King's College London
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0573-4
• 发表日期: 2012
• 页码: 157-186
• 关键词: stochastic-programming-problems; epi-convergent discretizations; transaction costs; Risk measures; fundamental theorem; securities markets; American options; DISCRETE-TIME; no-arbitrage; Duality

摘要

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.