Balbás, AlejandroBalbás, BeatrizBalbás, Raquel2012-01-162012-01-162010-09Journal of Computational and applied mathematics, 2010, v. 234, nº 10, pp. 2924-29310377-0427https://hdl.handle.net/10016/12974The minimization of risk functions is becoming a very important topic due to its interesting applications in Mathematical Finance and Actuarial Mathematics. This paper addresses this issue in a general framework. Many types of risk function may be involved. A general representation theorem of risk functions is used in order to transform the initial optimization problem into an equivalent one that overcomes several mathematical caveats of risk functions. This new problem involves Banach spaces but a mean value theorem for risk measures is stated, and this simplifies the dual problem. Then, optimality is characterized by saddle point properties of a bilinear expression involving the primal and the dual variable. This characterization is significantly different if one compares it with previous literature. Furthermore, the saddle point condition very easily applies in practice. Four applications in finance and insurance are presented.application/pdfengRisk minimizationSaddle point conditionActuarial and finantial aplicationsresearch articleEmpresa10.1016/j.cam.2010.04.002open access2924102931Journal of Computational and applied mathematics234