This paper proposes a novel analytical pricing–hedging framework for volatility derivatives which simultaneously takes into account rough and jumps. Directly targeting the instantaneous variance of risky asset, our model consists generalized fractional Ornstein–Uhlenbeck process driven by Lévy subordinator an independent sinusoidal-composite process, allows characteristic function average forwa...

We extend the recently developed rough path theory for Volterra equations from [F. Harang and S. Tindel, driven by signals, Stoch. Process. Appl. 142 (2021) 34–78] to case of more noise and/or singular kernels. It was already observed in that introduced there did not satisfy any geometric relation, similar classical theory. Thus, an extension irregular driving signals requires a deeper understa...

Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz spa...

Abstract. Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and “radial basis functions” stemming from the smooth kernel are intended to approximate only functions from this small native space. Therefore their approximation power is quite limited. Recently, Narcowich, Schaback and Ward [NSW], and Narcowich and Ward [NW], respectively,...

Plants have duplicate versions of the oxidative pentose phosphate pathway (oxPPP) enzymes with a subset localized to the chloroplast. The chloroplast oxPPP provides NADPH and pentose sugars for multiple metabolic pathways. This study identified two loss-of-function alleles of the Zea mays (maize) chloroplast-localized oxPPP enzyme 6-phosphogluconate dehydrogenase (6PGDH). These mutations caused...

Let h(y) be a bounded radial function and Ω (y ′) an H 1 function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator µ Ω related to the Littlewood-Paley g−function is defined by µ Ω (f)(x) = ∞ 0 |F t (x)| 2 dt t 3 1 2 , (1) where F t (x) = |x−y|≤t Ω (x − y) |x − y| d−1 h (|x − y|) f (y)dy (2) and h(y) ∈ L ∞ (R +). In this paper, we prove that the o...

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...