Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy by Meng Li, Xuefeng Wang, Fangfang Sun

“…The observed price advantage is stronger when the underlying asset has more volatility or when the asset price follows closer to Geometric Brownian Motion. Additionally, we found that a higher frequency trading strategy has stronger price advantage if there is no trading cost. …”
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Numerical Solutions of Micropolar Nanofluid over an Inclined Surface Using Keller Box Analysis by Khuram Rafique, Hammad Alotaibi, Taher A. Nofal, Muhammad Imran Anwar, Masnita Misiran, Ilyas Khan

“…The Brownian motion and thermophoretic impacts attained a noticeable intention of the recent researchers because these factors trigger the thermal conductivity of the nanofluid. …”
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Local time statistics and permeable barrier crossing: From Poisson to birth-death diffusion equations by Toby Kay, Luca Giuggioli

“…We bridge this gap by developing a microscopic representation of Brownian motion in the presence of permeable barriers that allows us to treat barriers with constant asymmetric permeabilities. …”
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A Swarm Robotic Exploration Strategy Based on an Improved Random Walk Method by Bao Pang, Yong Song, Chengjin Zhang, Hongling Wang, Runtao Yang

“…The random walk methods that are used most commonly are Brownian motion and Lévy flight, both of which mimic the self-organized behavior of social insects. …”
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Enhanced heat transfer and flow dynamics of Powell-Eyring nanofluid: unsteady stretched surface and with Stefan blowing/suction by Kalyan Kumar Challa, M. Eswara Rao, Muhammad Jawad, Taoufik Saidani, Suhad Ali Osman Abdallah, Thenmozhi D

“…New aspects related to Brownian motion and thermophoresis with heat transfer are examined. …”
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Entropy framework of the bioconvective Williamson nanofluid flow over a Riga plate with radiation, triple stratification and swimming microorganisms by K. Loganathan, N. Thamaraikannan, S. Eswaramoorthi, Reema Jain

“…The flow pattern model takes into account the influences of thermal radiation, Cattaneo-Christov heat and mass fluxes, stratifications, thermophoresis, and Brownian motion. Utilizing a suitable conversion approach, translate the partial differential equation (PDEs) system into ordinary differential equations (ODEs). …”
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Zero and Nonzero Mass Flux Effects of Bioconvective Viscoelastic Nanofluid over a 3D Riga Surface with the Swimming of Gyrotactic Microorganisms by T. S. Karthik, K. Loganathan, A. N. Shankar, M. Jemimah Carmichael, Anand Mohan, Mohammed K. A. Kaabar, Safak Kayikci

“…Results of interest such as the modified Hartmann number, mixed convection parameter, bioconvection Rayleigh number, and Brownian motion parameter are discussed in terms of various profiles. …”
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On the projections of Laplacians under Riemannian submersions by Huiling Le

“…Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.…”
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Theoretical analysis of MHD Maxwell two phase nano flow subject to viscous dissipation and chemical reaction: A nonsimilar approach by Muhammad Idrees Afridi, Gurram Dharmaiah, Jupudi Lakshmi Rama Prasad, Nallapati Vedavathi

“…The dimensionless concentration tends to decrease with Brownian motion. Its potential applications include medical sciences, microelectronics, biomedicine and various industrial processes.…”
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Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…Temperatures are significantly enhanced with radiative parameter. Increasing Brownian motion parameter depletes concentration values. …”
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Stock volatility as an anomalous diffusion process by Rubén V. Arévalo, J. Alberto Conejero, Òscar Garibo-i-Orts, Alfred Peris

“…Our model computes the diffusion exponent of a financial time series to measure its volatility and it categorizes market movements into five diffusion models: annealed transit time motion (ATTM), continuous time random walk (CTRW), fractional Brownian motion (FBM), Lévy walk (LW), and scaled Brownian motion (SBM).Our findings suggest that the diffusion exponent derived from anomalous diffusion processes provides insightful and novel perspectives on stock market volatility. …”
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Relationships of convolution products, generalized transforms, and the first variation on function space by Seung Jun Chang, Jae Gil Choi

“…We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. …”
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An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model by A. S. Deakin, Matt Davison

“…The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.…”
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Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme by Faiz Faizullah

“…We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions Xk of G-SFDEs are given. …”
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Topology of Locally and Non-Locally Generalized Derivatives by Dimiter Prodanov

“…There is a need for such generalizations when dealing with physical phenomena, such as fractures, shock waves, turbulence, Brownian motion, etc.…”
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Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps by Panhong Cheng, Zhihong Xu

“…In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. …”
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An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations by Weifeng Wang, Lei Yan, Junhao Hu, Zhongkai Guo

“…In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.…”
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Multivalued Impulsive SDEs Driven by G-Brownian Noise: Periodic Averaging Result by Mahmoud Abouagwa, Anas D. Khalaf, Nadia Gul, Sultan Alyobi, Al-Sharef Mohamed

“…This paper aims to study two approximation theorems in view of the periodic averaging results for non-Lipschitz multivalued stochastic differential equations with impulses and G-Brownian motion (MISDEGs). By adopting G-Itô’s formula and non-Lipschitz condition, the solutions to the simplified MSDEGs without impulses may replace those of the initial MISDEGs in view of approximation in L2-sense and capacity. …”
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On the Expected Discounted Penalty Function Using Physics-Informed Neural Network by Jiayu Wang, Houchun Wang

“…The discount rate is modeled by a Poisson process and a standard Brownian motion. By applying the differentiation method and total expectation formula, we obtain an integrodifferential equation for the expected discounted penalty function. …”
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Time slot-based RED algorithm on self-similar flows:SFRED by WANG Hui, JI Zhen-zhou, SUN Yan-dong, WANG Yuan-zheng

“…Based on fractional Brownian motion（FBM）,one calculation of the packet drop probability in the RED algorithm was derived under self-similar flows.Based on the self-similarity and the long-range dependence characteristics of Internet network traffics,a time slot-based RED algorithm on self-similar flows（SFRED） was proposed to the router queue management.The packet drop probability is calculated in every time-slot so that the burden is greatly reduced.It is simulated by NS2 and the experimental results show that the algorithm SFRED outperforms RED.SFRED can control the queue length under adaptive flows with a good throughput.…”
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