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Minimax strategies and duality with applications in financial mathematics

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Abstract

Many topics in Actuarial and Financial Mathematics lead to Minimax or Maximin problems (risk measures optimization, ambiguous setting, robust solutions, Bayesian credibility theory, interest rate risk, etc.). However, minimax problems are usually difficult to address, since they may involve complex vector spaces or constraints. This paper presents an unified approach so as to deal with minimax convex problems. In particular, we will yield a dual problem providing necessary and sufficient optimality conditions that easily apply in practice. Both, duals and optimality conditions are significantly simplified by drawing on the representation of probability measures on convex sets by points, classic problem for Choquet integrals. Important applications in risk analysis are given.

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Authors and Affiliations

  1. Académico Correspondiente de la Real Academia de Ciencias, University Carlos III of Madrid, C/ Madrid, 126, 28903, Getafe, Madrid, Spain

    Alejandro Balbás

  2. Department of Actuarial and Financial Economics, Complutense University of Madrid, Somosaguas Campus, 28223, Pozuelo de Alarcón, Madrid, Spain

    Raquel Balbás

Authors
  1. Alejandro Balbás
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  2. Raquel Balbás
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Correspondence to Raquel Balbás.

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Balbás, A., Balbás, R. Minimax strategies and duality with applications in financial mathematics. RACSAM 105, 291–303 (2011). https://doi.org/10.1007/s13398-011-0038-2

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  • DOI: https://doi.org/10.1007/s13398-011-0038-2

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Mathematics Subject Classification (2000)

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