An optimal transportation approach for assessing almost stochastic order

When stochastic dominance $F\leq_{st}G$ does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the $L_2-$Wasserstein distance, $\mathcal W_2$, to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a $\mathcal W_2$-based index of disagreement with stochastic order, $\varepsilon_{\mathcal W_2}(F,G)$. We provide asymptotic results allowing to test $H_0: \varepsilon_{\mathcal W_2}(F,G)\geq \varepsilon_0$ vs $H_a: \varepsilon_{\mathcal W_2}(F,G)<\varepsilon_0$, that, under rejection, would give statistical guarantee of almost stochastic dominance. We include a simulation study showing a good performance of the index under the normal model

Quadratic optimal functional quantization of stochastic processes and numerical applications

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.Comment: 41 page