Topic outline

  • Purpose of research

  • Achievements

     Equivalent conditions were established guaranteeing the validity of some types of integral inequalities such as Jensen, Chebyshev, Holder, Minkowski or Carlson for the generalized Sugeno integrals and Choquet integrals with respect to distortion monotone measures. Theorems on the subadditivity of the Sugeno integral for comonotone functions and any functions were given. All operations for which the seminormed Sugeno integralis +-additive were characterized. The properties of risk measures and insurance premiums for functionals specified in the prospect theory of Kahneman and Tversky as well as of a measure of risk aversion with imprecise data were examined. The impact of claim dependence on insurance products valuation was studied for some models of incomplete knowledge on the observation dependence structure.

    • References for research areas

    • International projects

      Wymiana Bilateralna Naukowców (NAWA) z krajem Słowacja, PPN/BIL/2018/1/00049/U/00001.