Optimal quantization for the pricing of swing options

In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz algorithm.Comment: 27

Introduction to vector quantization and its applications for numerics*

Proceedings of CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches. : T. Lelièvre et al. EditorsInternational audienceWe present an introductory survey to optimal vector quantization and its first applications to Numerical Probability and, to a lesser extent to Information Theory and Data Mining. Both theoretical results on the quantization rate of a random vector taking values in ℝd (equipped with the canonical Euclidean norm) and the learning procedures that allow to design optimal quantizers (CLVQ and Lloyd’s procedures) are presented. We also introduce and investigate the more recent notion of greedy quantization which may be seen as a sequential optimal quantization. A rate optimal result is established. A brief comparison with Quasi-Monte Carlo method is also carried out

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

Mitochondrial fission as a driver of stemness in tumor cells : mDIVI1 inhibits mitochondrial function, cell migration and cancer stem cell (CSC) signalling

Mitochondria are dynamic organelles frequently undergoing fission and fusion events to maintain their integrity, bioenergetics and spatial distribution, which is fundamental to the processes of cell survival. Disruption in mitochondrial dynamics plays a role in cancer. Therefore, proteins involved in regulating mitochondrial dynamics are potential targets for treatment. mDIVI1 is an inhibitor of the mitochondrial fission protein DRP1, which induces i) mitochondrial oxidative stress and ii) effectively reduces mitochondrial metabolism. We show here that mDIVI1 is able to inhibit 3D tumorsphere forming capacity, cell migration and stemness-related signalling in breast cancer cells, indicating that mDIVI1 can potentially be used for the therapeutic elimination of cancer stem cells (CSCs)

A multi-approach survey as the most reliable tool to accurately assess biodiversity: an example of thai murine rodents

Wildlife surveys rely on an accurate taxonomic framework. Identification tools used to reach this goal are not equivalent and may depend on several objectives and constraints, including sampling conservation difficulties, the invasiveness of the sampling techniques, sampling capacity, the relevance of the results, materials needed, the cost and the user time required in the field and laboratory. This article presents and discusses the advantages and limits of each identification tool used in the Ceropath (Community ecology of rodents and their pathogens in South East Asia) program to reach a fast and relevant identification of the rodents sampled. It is concluded that there needs to be a combination of the results from different methods, including the most recent ones, to achieve an improvement in taxonomic identification

Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

Vascular endothelial growth factor-A and Poly(A) binding protein-interacting protein 2 expression in human head and neck carcinomas: correlation and prognostic significance

Vascular endothelial growth factor-A (VEGF-A) has been demonstrated to play an important role in tumour angiogenesis and to influence prognosis in many cancers. However its prognostic value in head and neck squamous cell carcinomas (HNSCCs) remains controversial. Therefore, we investigated the clinical relevance of VEGF-A expression in HNSCCs and analysed whether its expression was associated with PAIP2 protein levels, a VEGF-A mRNA-binding partner that strongly regulates VEGF-A expression in tissue culture. We determined the correlation of VEGF-A and PAIP2 protein levels, quantitatively evaluated in tumour tissue homogenates from 54 patients with HNSCC, to clinicopathological parameters. We showed that VEGF-A expression in HNSCC is correlated to the stage of tumour differentiation (P=0.050) and is an independent prognostic factor for progression-free survival (P=0.001) and overall survival (P=0.0004). In a pharynx carcinoma cell line, we demonstrated by RNA interference that VEGF-A expression is closely controlled by PAIP2. Moreover, in human HNSCCs, VEGF-A expression is significantly correlated to PAIP2 protein levels (P=0.0018). Nevertheless, PAIP2 expression is associated with neither clinicopathological factors nor patient's survival. Our data suggest that, in contrast to PAIP2 protein levels, which are unrelated to tumour prognosis, VEGF-A expression could serve as a prognostic marker in head and neck cancer and may be helpful for targeted therapies

Dispersion and collapse in stochastic velocity fields on a cylinder

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is such that when the radius of the cylinder tends to infinity the fluid particles separate in an explosive way. Nevertheless, when the radius is finite the transition probability of the two-particle separation converges to an invariant measure. This behavior is due to the large-scale compressibility generated by the compactification of one dimension of the space

Detecting the impacts of harbour construction on a seagrass habitat and its subsequent recovery

Managing coastal development requires a set of tools to adequately detect ecosystem and water column degradation, but it also demands tools to detect any post-disturbance improvement. Structural seagrass indicators (such as shoot density or cover) are often used to detect or assess disturbances, but while they may be very sensitive to the impact itself, it is unclear if those indicators on their own can effectively reflect recovery at time scales relevant to managers. We used the construction of a harbour affecting a nearby Posidonia oceanica seagrass community to test the ability of a set of indicators (structural and others) to detect alterations and to evaluate their sensitivity to recovery of environmental quality after harbour construction was complete and the disturbance ceased. We used a Beyond Before After Control Impact (BBACI) design to evaluate effects on one impacted and three control meadows where we used structural, morphological, community and physiological indicators (26 in total) to asses disturbance impacts. Additionally, we measured some of the potential environmental factors that could be altered during and after the construction of the harbour and are critical to the survival of the seagrass meadow (light, sediment organic matter, sediment accrual). Harbour construction caused a clear increase in sediment organic matter and in sediment deposition rates, especially fine sand. Light availability was also reduced due to suspended sediments. Sediment and light conditions returned to normal levels 5 and 15 months after the construction began. As expected, seagrass structural indicators responded unequivocally to these environmental changes, with clear reductions in shoot density. Additionally, reduced light conditions quickly resulted in a decline in carbohydrate content in affected meadows. Unexpectedly, we also recorded a significant increase in metal content in plant tissues. No response was detected in the physiological indicators related to eutrophication (e.g. N and P content in tissues) and in morphological (shoot biomass) and community (epiphyte biomass) indicators. More than three years after the completion of the harbour, structural indicators did not show any sign of recovery. In contrast, physiological indicators, mainly heavy metal and carbohydrates content, were much better in detecting the improvement of the environmental conditions over the fairly short period of this study. These results indicate that while structural indicators are critical to evaluate the immediate effect of disturbances and the recovery on impacted systems, specific physiological indicators may be much better suited to determining the timing of environmental quality recovery. The design of impact and monitoring protocols in the wake of coastal developmental projects need to consider the differential effectiveness and time-response of measured indicators carefully