Numerical approximation of BSDEs using local polynomial drivers and branching processes

We propose a new numerical scheme for Backward Stochastic Differential Equations based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the Picard iteration can be solved by using a representation in terms of branching diffusion systems, thus avoiding the need for a fine time discretization. In contrast to the previous literature on the numerical resolution of BSDEs based on branching processes, we prove the convergence of our numerical scheme without limitation on the time horizon. Numerical simulations are provided to illustrate the performance of the algorithm.Comment: 28 page

Blockade of myeloid differentiation 2 attenuates diabetic nephropathy by reducing activation of the renin-angiotensin system in mouse kidneys

Background and Purpose: Both innate immunity and the renin-angiotensin system (RAS) play important roles in the pathogenesis of diabetic nephropathy (DN). Myeloid differentiation factor 2 (MD2) is a co-receptor of toll-like receptor 4 (TLR4) in innate immunity. While TLR4 is involved in the development of DN, the role of MD2 in DN has not been characterized. It also remains unclear whether the MD2/TLR4 signalling pathway is associated with RAS activation in diabetes. Experimental Approach: MD2 was blocked using siRNA or the low MW inhibitor, L6H9, in renal proximal tubular cells (NRK-52E cells) exposed to high concentrations of glucose (HG). In vivo, C57BL/6 and MD2−/− mice were injected with streptozotocin to induce Type 1 diabetes and nephropathy. Key Results: Inhibition of MD2 by genetic knockdown or the inhibitor L6H9 suppressed HG-induced expression of ACE and angiotensin receptors and production of angiotensin II in NRK-52E cells, along with decreased fibrosis markers (TGF-β and collagen IV). Inhibition of the MD2/TLR4-MAPKs pathway did not affect HG-induced renin overproduction. In vivo, using the streptozotocin-induced diabetic mice, MD2 was overexpressed in diabetic kidney. MD2 gene knockout or L6H9 attenuated renal fibrosis and dysfunction by suppressing local RAS activation and inflammation. Conclusions and Implications: Hyperglycaemia activated the MD2/TLR4-MAPKs signalling cascade to induce renal RAS activation, leading to renal fibrosis and dysfunction. Pharmacological inhibition of MD2 may be considered as a therapeutic approach to mitigate DN and the low MW inhibitor L6H9 could be a candidate for such therapy

Hedging of options with market impact and Numerical schemes of BSDEs using particle systems

La théorie classique de la valorisation des produits dérivés se repose sur l'absence de coûts de transaction et une liquidité infinie. Ces hypothèses sont toutefois ne plus véridiques dans le marché réel, en particulier quand la transaction est grande et les actifs non-liquides. Dans ce marché imparfait, on parle du prix de sur-réplication puisque la couverture parfaite est devenue parfois infaisable.La première partie de cette thèse se concentre sur la proposition d’un modèle qui intègre à la fois le coût de transaction et l’impact sur le prix du sous-jacent. Nous commençons par déduire la dynamique de l’actif en temps continu en tant que la limite de la dynamique en temps discret. Sous la contrainte d’une position nulle sur l’actif au début et à la maturité, nous obtenons une équation quasi-linéaire pour le prix du dérivé, au sens de viscosité. Nous offrons la stratégie de couverture parfaite lorsque l’équation admet une solution régulière. Quant à la couverture d’une option européenne “covered” sous la contrainte gamma, le principe de programme dynamique utilisé précédemment n'est plus valide. En suivant les techniques du cible stochastique et de l’équation différentielle partielle, nous démontrons que le prix de la sur-réplication est devenue une solution de viscosité d’une équation non linéaire de type parabolique. Nous construisons également la stratégie ε-optimale, et proposons un schéma numérique.La deuxième partie de cette thèse est consacrée aux études sur un nouveau schéma numérique d'EDSR, basé sur le processus de branchement. Nous rapprochons tout d’abord le générateur Lipschitzien par une suite de polynômes locaux, puis appliquons l’itération de Picard. Chaque itération de Picard peut être représentée en termes de processus de branchement. Nous démontrons la convergence de notre schéma sur l’horizon temporel infini. Un exemple concret est discuté à la fin dans l’objectif d’illustrer la performance de notre algorithme.Classical derivatives pricing theory assumes frictionless market and infinite liquidity. These assumptions are however easily violated in real market, especially for large trades and illiquid assets. In this imperfect market, one has to consider the super-replication price as perfect hedging becomes infeasible sometimes.The first part of this dissertation focuses on proposing a model incorporating both liquidity cost and price impact. We start by deriving continuous time trading dynamics as the limit of discrete rebalancing policies. Under the constraint of holding zero underlying stock at the inception and the maturity, we obtain a quasi-linear pricing equation in the viscosity sense. A perfect hedging strategy is provided as soons as the equation admits a smooth solution. When it comes to hedging a covered European option under gamma constraint, the dynamic programming principle employed previously is no longer valid. Using stochastic target and partial differential equation smoothing techniques, we prove the super-replication price now becomes the viscosity solution of a fully non-linear parabolic equation. We also show how ε-optimal strategies can be constructed, and propose a numerical resolution scheme.The second part is dedicated to the numerical resolution of the Backward Stochastic Differential Equation (BSDE). We propose a purely forward numerical scheme, which first approximates an arbitrary Lipschitz driver by local polynomials and then applies the Picard iteration to converge to the original solution. Each Picard iteration can be represented in terms of branching diffusion systems, thus avoiding the usual estimation of conditional expectation. We also prove the convergence on an unlimited time horizon. Numerical simulation is also provided to illustrate the performance of the algorithm

Couverture d'options dans un marché avec impact et schémas numériques pour les EDSR basés sur des systèmes de particules

Classical derivatives pricing theory assumes frictionless market and infinite liquidity. These assumptions are however easily violated in real market, especially for large trades and illiquid assets. In this imperfect market, one has to consider the super-replication price as perfect hedging becomes infeasible sometimes.The first part of this dissertation focuses on proposing a model incorporating both liquidity cost and price impact. We start by deriving continuous time trading dynamics as the limit of discrete rebalancing policies. Under the constraint of holding zero underlying stock at the inception and the maturity, we obtain a quasi-linear pricing equation in the viscosity sense. A perfect hedging strategy is provided as soons as the equation admits a smooth solution. When it comes to hedging a covered European option under gamma constraint, the dynamic programming principle employed previously is no longer valid. Using stochastic target and partial differential equation smoothing techniques, we prove the super-replication price now becomes the viscosity solution of a fully non-linear parabolic equation. We also show how ε-optimal strategies can be constructed, and propose a numerical resolution scheme.The second part is dedicated to the numerical resolution of the Backward Stochastic Differential Equation (BSDE). We propose a purely forward numerical scheme, which first approximates an arbitrary Lipschitz driver by local polynomials and then applies the Picard iteration to converge to the original solution. Each Picard iteration can be represented in terms of branching diffusion systems, thus avoiding the usual estimation of conditional expectation. We also prove the convergence on an unlimited time horizon. Numerical simulation is also provided to illustrate the performance of the algorithm.La théorie classique de la valorisation des produits dérivés se repose sur l'absence de coûts de transaction et une liquidité infinie. Ces hypothèses sont toutefois ne plus véridiques dans le marché réel, en particulier quand la transaction est grande et les actifs non-liquides. Dans ce marché imparfait, on parle du prix de sur-réplication puisque la couverture parfaite est devenue parfois infaisable.La première partie de cette thèse se concentre sur la proposition d’un modèle qui intègre à la fois le coût de transaction et l’impact sur le prix du sous-jacent. Nous commençons par déduire la dynamique de l’actif en temps continu en tant que la limite de la dynamique en temps discret. Sous la contrainte d’une position nulle sur l’actif au début et à la maturité, nous obtenons une équation quasi-linéaire pour le prix du dérivé, au sens de viscosité. Nous offrons la stratégie de couverture parfaite lorsque l’équation admet une solution régulière. Quant à la couverture d’une option européenne “covered” sous la contrainte gamma, le principe de programme dynamique utilisé précédemment n'est plus valide. En suivant les techniques du cible stochastique et de l’équation différentielle partielle, nous démontrons que le prix de la sur-réplication est devenue une solution de viscosité d’une équation non linéaire de type parabolique. Nous construisons également la stratégie ε-optimale, et proposons un schéma numérique.La deuxième partie de cette thèse est consacrée aux études sur un nouveau schéma numérique d'EDSR, basé sur le processus de branchement. Nous rapprochons tout d’abord le générateur Lipschitzien par une suite de polynômes locaux, puis appliquons l’itération de Picard. Chaque itération de Picard peut être représentée en termes de processus de branchement. Nous démontrons la convergence de notre schéma sur l’horizon temporel infini. Un exemple concret est discuté à la fin dans l’objectif d’illustrer la performance de notre algorithme

Metabolomics Combined with Transcriptomics Analysis Revealed the Amino Acids, Phenolic Acids, and Flavonol Derivatives Biosynthesis Network in Developing Rosa roxburghii Fruit

Rosa roxburghii Tratt. is a specific fruit with high nutritional value and antioxidative activities. However, the key metabolites and their biosynthesis are still unknown. Herein, a main cultivated variety, ‘Guinong 5’ (Rr5), was chosen to analyze the metabolomics of the three developmental stages of R. roxburghii fruit by liquid chromatography–tandem mass spectrometry (LC-MS/MS). A total of 533 metabolites were identified, of which 339 were significantly altered. Total phenols, flavonoids, and amino acids were significantly correlated to at least one in vitro antioxidant activity. The conjoint Kyoto Encyclopedia of Genes and Genomes (KEGG) co-enrichment analysis of metabolome and transcriptome was focused on amino acid, phenylpropanoid, and flavonoid biosynthesis pathways. The amino acid, phenolic acid, and flavonol biosynthesis networks were constructed with 32 structural genes, 48 RrMYBs, and 23 metabolites. Of these, six RrMYBs correlated to 9–15 metabolites in the network were selected to detect the gene expression in six different R. roxburghii genotypes fruits. Subsequently, 21 key metabolites were identified in the in vitro antioxidant activities in the fruits at various developmental stages or in fruits of different R. roxburghii genotypes. We found that four key RrMYBs were related to the significantly varied amino acids, phenolic acids, and flavonol derivatives in the network during fruit development and the key metabolites in the in vitro antioxidative activities in the fruits of six R. roxburghii genotypes. This finding provided novel insights into the flavonoid, polyphenol, and amino acid synthesis in R. roxburghii

Parallel β‑Sheet Fibril and Antiparallel β‑Sheet Oligomer: New Insights into Amyloid Formation of Hen Egg White Lysozyme under Heat and Acidic Condition from FTIR Spectroscopy

Hen egg white lysozyme (HEWL) is widely used as a model protein for amyloid research. In this study, we aim to use Fourier transform infrared (FTIR) spectroscopy to gain new structural insights into amyloid formation of HEWL under heat and acidic condition. We reveal that the fibril-forming solution of HEWL has the capability to form fibril and oligomer with distinct β-sheet configurations under different temperatures. Amyloid fibril with parallel β-sheet configuration is formed at elevated temperature, while oligomer with antiparallel β-sheet configuration is formed at room temperature. The interplay between fibrillation and oligomerization suggests that the two β-sheet aggregates consume the same amyloidogenic materials such as peptide fragments and nicked HEWL due to lysozyme hydrolysis under heat and acidic condition. Temperature-dependent FTIR reveals that the oligomer is unstable at elevated temperature, demonstrating its off-pathway nature. The temperature-dependent formation of parallel and antiparallel β-sheet configurations discovered in lysozyme system is compared with that of amyloid-β and α-synuclein systems and the implication is discussed

Interaction Mechanism of the Upper and Lower Main Roofs with Different Properties in Close Coal Seams: A Case Study

Close-distance coal seams are widely distributed in China, and the mining of overlying coal seams leads to floor damage. To grasp the properties and the fracture spans of the damaged main roof in the underlying coal seam, combining the calculation of the floor damage depth with rock damage theory and the formulas for calculating the first and periodic weighting intervals of the damaged main roof and the instability conditions of the damaged key blocks are obtained. Three interaction stability mechanics models are proposed for key blocks with different properties of the upper and lower main roof, and the instability conditions of the lower damaged key blocks are obtained when the fracture lines overlap. When combined with a specific example, the field monitoring verified the calculation results. The research results are as follows: (1) The first and periodic weighting intervals, horizontal thrust between blocks, and critical load of instability of the damaged main roof are significantly reduced. Still, there are differences in its reduction under different loads, rotation angles, and lumpiness. (2) When the fracture lines of the upper and lower main roofs overlap, the stability of the damaged key blocks is the lowest. There are three linkage stability regions in the critical load curves of the two key blocks. (3) In this case, the damage equivalent of the main roof is 0.397, which belongs to the local damage type. Its first and periodic weighting intervals are 40 m and 16 m, which is 22% and 24% less than when there is no damage. (4) A supporting load of 0.489 MPa is required to maintain the stability of the upper key block, and the lower damaged key block is prone to rotary and sliding instability during the first and periodic weighting, respectively. Thus, the supports need to bear a total of 0.988 MPa and 0.761 MPa to maintain the stability of the two key blocks simultaneously. The ground pressure data monitored on-site is in accord with the calculation results

The global power sector’s low-carbon transition may enhance sustainable development goal achievement

Abstract The low-carbon power transition, which is key to combatting climate change, has far-reaching effects on achieving the Sustainable Development Goals (SDGs) in terms of issues such as resource use, environmental emissions, employment, and many more. Here, we assess the potential impacts of the power transition on progress toward achieving multiple SDGs (covering 18 targets across the 17 goals) across 49 economies under nine socioeconomic and climate scenarios. We find that the low-carbon power transition under the representative concentration pathway (RCP)2.6 scenarios could lead to an approximately 11% improvement in the global SDG index score from 54.70 in 2015 to 59.89-61.33 in 2100. However, the improvement would be significantly decreased to 4.42%-7.40% and 7.55%-8.93% under the RCP6.0 and RCP4.5 scenarios, respectively. The power transition could improve the overall SDG index in most developed economies under all scenarios while undermining their resource-related SDG scores. Power transition-induced changes in international trade would improve the SDG progress of developed economies but jeopardize that of developing economies, which usually serve as resource hubs for meeting the demand for low-carbon power transition in developed economies

Low carbon transition of global power sector may enhance sustainable development goals

Low-carbon power transition, key to combatting climate change, brings far-reaching effects on achieving Sustainable Development Goals (SDGs), in terms of resources use, environmental emissions, employment, and many more. Here we assess the potential impacts of power transition on multiple SDGs progress across 49 economies under six socio-economic-climate scenarios. We find that the low carbon power transition under Representative Concentration Pathway (RCP) 2.6 scenarios could lead to approximately 10% improvement in global SDG index score from 65.30 in 2015 to 71.62–71.64 in 2050. However, the improvement would be significantly decreased to 1.91%-4.98% and 3.42%-5.24% under RCP6.0 and RCP4.5 scenarios, respectively. Power transition could improve the overall SDG index in most developed economies under all scenarios while undermine their resources-related SDG scores. The power transition induced changes in international trade would improve developed economies’ SDG progress, but jeopardize that of developing economies which usually serve as resource hubs to meet the demand for low carbon power transition in developed economies