A Boolean valued analysis approach to conditional risk

José Miguel Zapata

By means of the techniques of Boolean valued analysis, we provide a transfer
principle between duality theory of classical convex risk measures and duality
theory of conditional risk measures. Namely, a conditional risk measure can be
interpreted as a classical convex risk measure inside of a suitable
set-theoretic model. As a consequence, many properties of a conditional risk
measure can be interpreted as basic properties of convex risk measures.
This amounts to a method to interpret a theorem of dual representation of
convex risk measures as a new theorem of dual representation of conditional
risk measures. As an instance of application, we establish a general robust
representation theorem for conditional risk measures and study different
particular cases of it.