Stochastic orders in time transformed exponential models with applications

This paper studies expectations of a supermodular function of bivariate random risks following TTE models. Comparison of such expectations are conducted based on some stochastic orders of the involved univariate survival functions in the models, and also the upper orthant-convex order between two bivariate random risks in TTE models is built. This corrects Theorem 2.3 of Mulero et al. (2010) and invalidates some results there. Some applications in actuarial science are presented as well.