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.
optimization in banach spaces; min–max strategies; duality; applications in actuarial and financial mathematics