Comparison of option prices in semimartingale models (Q854274)

The authors derive an extension of the previous comparison results to \(d\)-dimensional semimartingales. They consider the convex ordering and also a variant of the convex ordering -- the directionally convex order -- which has turned out to be of particular interest for risk measures. A new technique is also developed that is based on discrete approximation by Euler schemes to establish the propagation of convexity property for several uni- and multi-variate processes, where the known techniques do not seem to be applicable. This leads to more general comparison results also for one-dimensional processes. In the case of jump diffusions this approach allows to establish a general comparison result which extends the coupling based results substantially.