In this paper a time-fractional Black–Scholes equation is examined. We transform the initial value problem into an equivalent integral–differential equation with a weakly singular kernel and use an integral discretization scheme on an adapted mesh for the time discretization. A rigorous analysis about the convergence of the time discretization scheme is given by taking account of the possibly singular behavior of the exact solution and first-order convergence with respect to the time variable is proved. For overcoming the possibly nonphysical oscillation in the computed solution caused by the degeneracy of the Black–Scholes differential operator, we employ a central difference scheme on a piecewise uniform mesh for the spatial discretization. It is proved that the scheme is stable and second-order convergent with respect to the spatial variable. Numerical experiments support these theoretical results.

Numerical approximation of a time-fractional Black–Scholes equation

While the arbitrage opportunity in the Black–Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black–Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black–Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann–Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

Arbitrage with fractional Gaussian processes

Simple Summary Essential oils can be used to improve animal performance as well as the health and quality of livestock products. The aim of this study was to evaluate the effects of essential oil supplementation on animal performance, ruminal fermentation, blood metabolites, and meat and milk quality of small ruminants through a meta-analysis. Supplementation with essential oils improved weight gain, milk production and composition, oxidative stability of meat, and blood serum antioxidant enzyme activity. Additionally, essential oils decreased methane emissions. This suggests that the inclusion of essential oils in the diets of small ruminants could be used to improve animal performance and the quality of meat and milk, in addition to reducing the environmental impact and oxidative stress of the animals. Abstract There is an increasing pressure to identify natural feed additives that improve the productivity and health of livestock, without affecting the quality of derived products. The objective of this study was to evaluate the effects of dietary supplementation with essential oils (EOs) on productive performance, rumen parameters, serum metabolites, and quality of products (meat and milk) derived from small ruminants by means of a meta-analysis. Seventy-four peer-reviewed publications were included in the data set. Weighted mean differences (WMD) between the EOs treatments and the control treatment were used to assess the magnitude of effect. Dietary inclusion of EOs increased (p < 0.05) dry matter intake (WMD = 0.021 kg/d), dry matter digestibility (WMD = 14.11 g/kg of DM), daily weight gain (WMD = 0.008 kg/d), and feed conversion ratio (WMD = −0.111). The inclusion of EOs in small ruminants’ diets decreased (p < 0.05) ruminal ammonia nitrogen concentration (WMD = −0.310 mg/dL), total protozoa (WMD = −1.426 × 105/mL), methanogens (WMD = −0.60 × 107/mL), and enteric methane emissions (WMD = −3.93 L/d) and increased ruminal propionate concentration (WMD = 0.726 mol/100 mol, p < 0.001). The serum urea concentration was lower (WMD = −0.688 mg/dL; p = 0.009), but serum catalase (WMD = 0.204 ng/mL), superoxide dismutase (WMD = 0.037 ng/mL), and total antioxidant capacity (WMD = 0.749 U/mL) were higher (p < 0.05) in response to EOs supplementation. In meat, EOs supplementation decreased (p < 0.05) the cooking loss (WMD = −0.617 g/100 g), malondialdehyde content (WMD = −0.029 mg/kg of meat), yellowness (WMD = −0.316), and total viable bacterial count (WMD = −0.780 CFU/g of meat). There was higher (p < 0.05) milk production (WMD = 0.113 kg/d), feed efficiency (WMD = 0.039 kg/kg), protein (WMD = 0.059 g/100 g), and lactose content in the milk (WMD = 0.100 g/100 g), as well as lower somatic cell counts in milk (WMD = −0.910 × 103 cells/mL) in response to EOs supplementation. In conclusion, dietary supplementation with EOs improves productive performance as well as meat and milk quality of small ruminants. In addition, EOs improve antioxidant status in blood serum and rumen fermentation and decrease environmental impact.

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Essential Oils as a Dietary Additive for Small Ruminants: A Meta-Analysis on Performance, Rumen Parameters, Serum Metabolites, and Product Quality

Option pricing under finite moment log stable process in a regulated market: A generalized fractional path integral formulation and Monte Carlo based simulation

In this work, we propose a numerical technique based on the Pade scheme for solving the two-sided space-fractional diffusion equation. First, space fractional diffusion equations are approximated with respect to space variable. We will achieve a system of ODE. Then by applying a parallel implementation of the A-stable methods, this system is solved. Also, we use of the presented method for pricing European call option under a geometric Levy process. Illustrative examples are included to show the accuracy and applicability of the new technique presented in the current paper.

The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing

An explicit closed-form analytical solution for European options under the CGMY model

The pelleted total mixed ration (PTMR) has a positive effect on the productivity of fattening lambs. However, whether the beneficial effects are underpinned by altering the rumen microbiota and metabolome that remain unclear. This study aimed to investigate correlations among growth performance, ruminal microbiota, and ruminal metabolome of lambs fed PTMR diet. A total of 100 crossbred (Dorper sheep × Fine-wool sheep) ram lambs at 55 days of age with similar body weight (BW) (13.2 ± 0.5 kg) were randomly allocated to 10 pens that were fed either PTMR (PTMR group) or unpelleted total mixed ration (UPTMR group) with the same dietary ingredients and nutritional contents. The average daily gain (ADG) and average daily feed intake (ADFI) were determined during the 62-day experimental period and ruminal pH, volatile fatty acid (VFA) concentrations, microbiota, and metabolome in the rumen of the lambs were examined at the end of the experiment. Compared to those of the UPTMR group, the PTMR group had greater ADFI (P = 0.002), ADG (P = 0.003), and feed efficiency (G/F) (P < 0.05). Similarly, feeding PTMR increased the concentration of total VFA (TVFA) and the molar proportion of propionate, but decreased the proportion of butyrate and acetate to propionate ratio in the rumen of lambs compared to that in lambs from the UPTMR group (P < 0.05). In addition, the PTMR group demonstrated lowered alpha-diversity of the ruminal microbiota and enhanced the relative abundance of Fibrobacter (P < 0.05), Veillonellaceae (P < 0.05), and the abundance of Rikenellaceae (P = 0.064) in the rumen compared with those in the UPTMR group. Feeding lambs with PTMR significantly upregulated the metabolic pathways involving tryptophan, histidine, cysteine and methionine, β-alanine, tyrosine metabolisms, and steroid biosynthesis. Moreover, the abundance of the microbiota strongly correlated with the altered performance, ruminal VFA, metabolites, and metabolic pathways of lambs. Taken together, feeding PTMR shaped the ruminal microbiota of lambs with decreased diversity, while improving relative abundance of some specific microbes and upregulating certain growth-related metabolic pathways, which contributed to the augmented growth performance and G/F of fattening lambs. Thus, feeding PTMR to fattening lambs for superior production performance and G/F is recommended.

/pdf/diet-type-impacts-production-performance-of-fattening-lambs-3aqlqs2v.pdf

Diet Type Impacts Production Performance of Fattening Lambs by Manipulating the Ruminal Microbiota and Metabolome

Robust optimization of stamping process based on Bayesian estimation

Stamping is a very important manufacturing process. To optimize the process parameters, a hybrid surrogate model based on the back-propagation neural network and sparse auto-encoder is proposed and compared with classical surrogate models to verify its reliability. Furthermore, the hybrid improved particle swarm optimization–genetic algorithm, based on chaos theory, is proposed and compared with other algorithms. A double-C part is used as an engineering example to verify the proposed method. The Latin hypercube sampling method is used for sampling and the response value is obtained by AutoForm simulation software. On this basis, the hybrid surrogate model is used to establish the mapping relationship between the forming quality of the double-C part and the stamping process parameters. The optimal stamping process parameters are obtained through the improved hybrid algorithm. The results demonstrate that the wrinkling of the optimized double-C part is significantly reduced and the forming quality is improved. 

Optimization of stamping process parameters based on an improved particle swarm optimization–genetic algorithm and sparse auto-encoder–back-propagation neural network model

Meiyu Du

Papers

An explicit closed-form analytical solution for European options under the CGMY model

Diet Type Impacts Production Performance of Fattening Lambs by Manipulating the Ruminal Microbiota and Metabolome

Robust optimization of stamping process based on Bayesian estimation

Optimization of stamping process parameters based on an improved particle swarm optimization–genetic algorithm and sparse auto-encoder–back-propagation neural network model

Analysis and optimization of the stamping process with pretreated 7A09 aluminum alloy