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8126 results in Fluid dynamics and solid mechanics

Page 21 of 407

  • AN IMEX-BASED APPROACH FOR THE PRICING OF EQUITY WARRANTS UNDER FRACTIONAL BROWNIAN MOTION MODELS

  • Part of
  • WENTING CHEN, XIAOYING JIANG
  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 4 / October 2022
    Published online by Cambridge University Press:
    23 August 2023, pp. 380-393

  • In this paper, the pricing of equity warrants under a class of fractional Brownian motion models is investigated numerically. By establishing a new nonlinear partial differential equation (PDE) system governing the price in terms of the observable stock price, we solve the pricing system effectively by a robust implicit-explicit numerical method. This is fundamentally different from the documented methods, which first solve the price with respect to the firm value analytically, by assuming that the volatility of the firm is constant, and then compute the price with respect to the stock price and estimate the firm volatility numerically. It is shown that the proposed method is stable in the maximum-norm sense. Furthermore, a sharp theoretical error estimate for the current method is provided, which is also verified numerically. Numerical examples suggest that the current method is efficient and can produce results that are, overall, closer to real market prices than other existing approaches. A great advantage of the current method is that it can be extended easily to price equity warrants under other complicated models.

  • 2 - Single-Phase Flow Equations and Regimes

  • Eric Loth, University of Virginia
  • Book:
    Fluid Dynamics of Particles, Drops, and Bubbles
    Published online:
    28 July 2023
    Print publication:
    17 August 2023, pp 35-83

  • Summary

    The primary assumptions and formulations for single-phase flow regimes are reviewed in this chapter. This includes the governing partial differential equations for general fluid dynamics (mass, momentum, energy, and species), equations of state and associated flow regimes, rotational effects and the stream function for incompressible flow, and viscous effects with the Reynolds number, including flow instability mechanisms.

  • 3 - Governing Equations for an Isolated Spherical Particle

  • Eric Loth, University of Virginia
  • Book:
    Fluid Dynamics of Particles, Drops, and Bubbles
    Published online:
    28 July 2023
    Print publication:
    17 August 2023, pp 84-129

  • Summary

    This chapter develops the point-force Equations of Motion for a single spherical particle moving in an unbounded fluid. This includes the particle Equations of Motion, which are considered as a sum of pointwise forces. The drag force is described for solid and fluid particles for Reynolds numbers ranging from creeping flow to turbulent flow. The three acceleration forces of added-mass, fluid-stress, and history forces are explained, and all the forces are combined to provide various Equations of Motion. Finally, heat and mass transfer effects on the particle are discussed.

Page 21 of 407