RT Journal Article
T1 Minimizing measures of risk by saddle point conditions
A1 Balbás, Alejandro
A1 Balbás, Beatriz
A1 Balbás, Raquel
AB The minimization of risk functions is becoming a very important topic due to its interestingapplications in Mathematical Finance and Actuarial Mathematics. This paper addressesthis issue in a general framework. Many types of risk function may be involved. Ageneral representation theorem of risk functions is used in order to transform the initialoptimization problem into an equivalent one that overcomes several mathematical caveatsof risk functions. This new problem involves Banach spaces but a mean value theoremfor risk measures is stated, and this simplifies the dual problem. Then, optimality ischaracterized by saddle point properties of a bilinear expression involving the primal andthe dual variable. This characterization is significantly different if one compares it withprevious literature. Furthermore, the saddle point condition very easily applies in practice.Four applications in finance and insurance are presented.
PB Elsevier
SN 0377-0427
YR 2010
FD 2010-09
LK https://hdl.handle.net/10016/12974
UL https://hdl.handle.net/10016/12974
LA eng
NO This research was partially supported by ‘‘Welzia Management SGIIC SA, RD_Sistemas SA’’ and ‘‘MEyC’’ (Spain), Grant ECO2009-14457-C04.
DS e-Archivo
RD 27 jul. 2024