Clark-Ocone type formula for non-semimartingales with finite quadratic variation

We provide a suitable framework for the concept of finite quadratic variation for processes with values in a separable Banach space $B$ using the language of stochastic calculus via regularizations, introduced in the case $B= \R$ by the second author and P. Vallois. To a real continuous process $X$ we associate the Banach valued process $X(\cdot)$, called {\it window} process, which describes the evolution of $X$ taking into account a memory $\tau>0$. The natural state space for $X(\cdot)$ is the Banach space of continuous functions on $[-\tau,0]$. If $X$ is a real finite quadratic variation process, an appropriated It\^o formula is presented, from which we derive a generalized Clark-Ocone formula for non-semimartingales having the same quadratic variation as Brownian motion. The representation is based on solutions of an infinite dimensional PDE

Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations

The paper reminds the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with "windows" of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution.Comment: arXiv admin note: text overlap with arXiv:1401.503

On stochastic calculus related to financial assets without semimartingales

This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus related to $\mathcal{A}$-martingales with some examples is developed. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. We finally revisit some no arbitrage conditions of Bender-Sottinen-Valkeila type

The physical oceanographic processes on the southeast African shelf and slope

Situated between the southeast coast of South Africa and the western edge of the Agulhas Current, is the southeast African shelf. The Agulhas Current, like other western boundary currents of the world, strongly influences the oceanographic conditions of its adjacent shelf system. Limited societal drivers have resulted in the southeast African shelf being one of the least studied and under-sampled shelf systems in southern Africa. The in situ sample deficit has led to the majority of studies conducted in this region to be carried out using satellite data and modelling. In order to identify the physical oceanographic processes occurring on the southeast African shelf and slope, as well as the influence that the Agulhas Current has on them, this study analysed satellite data combined with high resolution in situ data, acquired during two hydrographic surveys of the southeast African shelf and slope, during January/February (austral summer) and July/August (austral winter) 2017. The Agulhas Current as well as a number of physical processes were observed to influence the shelf region. The snapshot of the two seasons given by the January/February and July/August in situ data presented indications of seasonality of temperature and salinity within the upper water masses but not within the deeper water masses. The same five water masses, Tropical Surface Water (TSW), Subtropical Surface Water (STSW), South Indian Central Water (SICW), Red Sea Water (RSW) as well as Antarctic Intermediate Water (AAIW), were observed during each cruise. As a result of the westward widening shelf from just east of East London, divergence-induced upwelling was observed between the coast and the inshore edge of the Agulhas Current, during both January/February and July/August. Ekman veering in the bottom boundary layer was observed between Port Alfred and East London during January/February as a result of the close proximity of the Agulhas Current to the slope. Altimetry data indicated the presence of a cyclonic eddy during both the January/February and July/August 2017 surveys. The presence of cold nutrient-rich SICW in the bottom layers on the shelf during January/February and July/August was as a result of the uplift caused by Ekman pumping associated with the cyclonic eddies. AAIW, usually observed along the offshore edge of the Agulhas Current, was found on the slope along the inshore edge of the Agulhas Current, as a result of the presence of cyclonic eddies. Wind-driven upwelling, induced by offshore Ekman transport and vertical mixing, resulted in the surfacing of cooler waters from below at several locations. Chlorophyll-a concentrations were found to be higher during January/February than during July/August 2017. The dissolved oxygen levels observed on the shelf during both surveys were found to be in the range where the biological responses would be insignificant, suggesting that oxygen availability, on the southeast African shelf, adequately facilitates the survival of the existing shelf biology and that low oxygen conditions do not seem to impact the shelf. This study provides the description of the first high resolution shelf wide hydrographic surveys of the region, during the austral summer and winter (even though they are considered as snapshots) which sets a baseline of oceanographic conditions on the shelf as well as the processes affecting it. The results of this study can be used by the scientific community and governmental departments to better implement conservation regulations regarding marine protected areas in the region

A Quantitative MALDI-MSI Study of the Movement of Molecules in Biological Systems

The use of mass spectrometry imaging (MSI) for the analysis of 3D tissue models of human skin has been shown to provide an elegant label-free methodology for the study of both drug absorption and drug biotransformation. The main aim of the work presented in this thesis was to develop methodology for quantitative assessment of percutaneous absorption using matrix assisted laser desorption ionisation mass spectrometry imaging (MALDI-MSI). Quantitative assessment of the absorption of an antifungal agent, terbinafine hydrochloride, into the epidermal region of a commercial full thickness living skin equivalent model (Labskin) was used as a model system. Different approaches to generate robust and sensitive quantitative mass spectrometry imaging (QMSI) data were developed and compared. The combination of microspotting of analytical and internal standards, matrix sublimation, and recently developed software for quantitative mass spectrometry imaging provided a high-resolution method for the determination of terbinafine hydrochloride in Labskin. A quantitative assessment of the effect of adding a penetration enhancer (dimethyl isosorbide (DMI)) to the delivery vehicle was also performed, and data was compared to LC–MS/MS measurements of isolated epidermal tissue extracts. Comparison of means and standard deviations indicated no significant difference between the values obtained by the two methods. In this thesis the localisation of hydrocortisone hydrochloride in ex-vivo skin was also investigated. Hydrocortisone exhibits a low ionisation efficiency that makes its detection challenging with mass spectrometry techniques. An in-solution and on-tissue chemical derivatisation reaction using the Girard reagent T, a hydrazine based reagent, significantly increased the sensitivity and detection of the respective hydrocortisone-derivative using MALDI-MSI. In an additional study, MALDI-MSI was used to assess the metabolic activity in Labskin by employing the approach of "substrate-based mass spectrometry imaging" (SBMSI). Preliminary MALDI-MSI data detected the activity of the carboxylesterase 1 enzyme in the epidermal layer of skin. The MALDI-MSI data was supported by preliminary LC-MS/MS analysis. To investigate the reproducibility of the results future investigations are required

Infinite dimensional stochastic calculus via regularization

This paper develops some aspects of stochastic calculus via regularization to Banach valued processes. An original concept of $\chi$-quadratic variation is introduced, where $\chi$ is a subspace of the dual of a tensor product $B \otimes B$ where $B$ is the values space of some process $X$ process. Particular interest is devoted to the case when $B$ is the space of real continuous functions defined on $[-\tau,0]$, $\tau>0$. Itô formulae and stability of finite $\chi$-quadratic variation processes are established. Attention is deserved to a finite real quadratic variation (for instance Dirichlet, weak Dirichlet) process $X$. The $C([-\tau,0])$-valued process $X(\cdot)$ defined by $X_t(y) = X_{t+y}$, where $y \in [-\tau,0]$, is called {\it window} process. Let $T >0$. If $X$ is a finite quadratic variation process such that $[X]_t = t$ and $h = H(X_T(\cdot))$ where $H:C([-T,0])\longrightarrow \R$ is $L^{2}([-T,0])$-smooth or $H$ non smooth but finitely based it is possible to represent $h$ as a sum of a real $H_{0}$ plus a forward integral of type $\int_0^T \xi d^-X$ where $H_{0}$ and $\xi$ are explicitly given. This representation result will be strictly linked with a function $u:[0,T]\times C([-T,0])\longrightarrow \R$ which in general solves an infinite dimensional partial differential equation with the property $H_{0}=u(0, X_{0}(\cdot))$, $\xi_{t}=D^{\delta_{0}}u(t, X_{t}(\cdot)):=Du(t,X_{t}(\cdot))(\{0\})$. This decomposition generalizes the Clark-Ocone formula which is true when $X$ is the standard Brownian motion $W$. The financial perspective of this work is related to hedging theory of path dependent options without semimartingales

The perception of the illness and the self-efficacy in the management of emotions in cardiac patients

Cardiac rehabilitation is the sum of psychological, physical and social treatments that are offered to cardiac patients to maintain or regain an active position in society. This study wants to evaluate changes in the perception of the illness and in the self-efficacy of the management of positive and negative emotions in patients who went through cardiac rehabilitation. Sixty-seven patients (20 females, 47 males) were selected within the cardiac rehabilitation unit in the Hospital of Cittadella (Italy). Illness Perception Questionnaire - revised version and the Scale for the self-efficacy of the management of positive and negative emotions were submitted at the beginning and at the end of the rehabilitation program. One-way analyses-of-variance were performed to evaluate different answers in questionnaires between pre- and post-evaluation, and to explore gender differences. A significant change was found in the perception of duration of illness, perceived as permanent and longer after the cardiac rehabilitation program. Furthermore, at the end of the cardiac rehabilitation program men perceived the illness more chronic than women, even if they are less worried and anxious. Intensive cardiac rehabilitation has a great emotional impact on cardiac patients, influencing their perception and management of the illness. Working on emotions, through psychological groups, helps patients change their beliefs by offering them a different perspective to approach the illness