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Minimizing Vector Risk Measures

In: New Developments in Multiple Objective and Goal Programming

Author

Listed:
  • Alejandro Balbás

    (University Carlos III of Madrid)

  • Beatriz Balbás
  • Raquel Balbás

Abstract

The minimization of risk functions is becoming very important due to its interesting applications in Mathematical Finance and Actuarial Mathematics. This paper addresses this issue in a general framework. Vector optimization problems involving many types of risk functions are studied. The “balance space approach” of multiobjective optimization and a general representation theorem of risk functions is used in order to transform the initial minimization problem in an equivalent one that is convex and usually linear. This new problem permits us to characterize optimality by saddle point properties that easily apply in practice. Applications in finance and insurance are presented.

Suggested Citation

  • Alejandro Balbás & Beatriz Balbás & Raquel Balbás, 2010. "Minimizing Vector Risk Measures," Lecture Notes in Economics and Mathematical Systems, in: Dylan Jones & Mehrdad Tamiz & Jana Ries (ed.), New Developments in Multiple Objective and Goal Programming, pages 55-69, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-10354-4_4
    DOI: 10.1007/978-3-642-10354-4_4
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