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3869 results in Optimization

Page 18 of 194

  • APPROXIMATE PRICING OF DERIVATIVES UNDER FRACTIONAL STOCHASTIC VOLATILITY MODEL

  • Part of
  • Y. HAN, X. ZHENG
  • Journal:
    The ANZIAM Journal / Volume 65 / Issue 3 / July 2023
    Published online by Cambridge University Press:
    15 January 2024, pp. 229-247

  • This paper examines the issue of derivative pricing within the framework of a fractional stochastic volatility model. We present a deterministic partial differential equation system to derive an approximate expression for the derivative price. The proposed approach allows for the stochastic volatility to be expressed as a composition of deterministic functions of time and a fractional Ornstein–Uhlenbeck process. We apply this method to the European option pricing under the fractional Stein–Stein volatility model, demonstrating its feasibility and reliability through numerical simulations. Our numerical simulations also illustrate the impact of the parameters in the fractional stochastic volatility model on the option price.

  • NONLINEAR SELF-MODULATION OF GRAVITY-CAPILLARY WAVES ON SHEAR CURRENTS IN FINITE DEPTH

  • Part of
  • TANMOY PAL, ASOKE KUMAR DHAR
  • Journal:
    The ANZIAM Journal / Volume 65 / Issue 3 / July 2023
    Published online by Cambridge University Press:
    12 January 2024, pp. 248-272

  • A nonlinear evolution equation correct to fourth order is developed for gravity-capillary waves on linear shear currents in finite water depth. Therefore, this equation covers both effects of depth uniform currents and uniform vorticity. Starting from this equation, an instability analysis is then made for narrow banded uniform Stokes waves. The notable feature is that our investigation due to fourth order shows a remarkable improvement compared with the third-order one, and produces an excellent result compatible with the exact result of Longuet-Higgins. We observe that linear shear currents considerably change the modulational instability properties of capillary-gravity waves, such as the growth rate and bandwidth of instability.

  • ON MODELLING WATER QUALITY WITH STOCHASTIC DIFFERENTIAL EQUATIONS

  • Part of
  • MAHMOUD B. A. MANSOUR
  • Journal:
    The ANZIAM Journal / Volume 65 / Issue 3 / July 2023
    Published online by Cambridge University Press:
    09 January 2024, pp. 273-284
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  • Based on biochemical kinetics, a stochastic model to characterize wastewater treatment plants and dynamics of river water quality under the influence of random fluctuations is proposed in this paper. This model describes the interaction between dissolved oxygen (DO) and biochemical oxygen demand (BOD), and is in the form of stochastic differential equations driven by multiplicative Gaussian noises. The stochastic persistence problem for the model of the system is analysed. Further, a numerical simulation of the stationary probability distributions of BOD and OD by approximations of the stochastic process solution is presented. These results have implications for the prediction and control of pollutants.

Model Risk Management
  • Risk Bounds under Uncertainty
  • Ludger Rüschendorf, Steven Vanduffel, Carole Bernard
  • Published online:
    21 December 2023
    Print publication:
    25 January 2024
  • This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference work for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development, identifying which ones require more attention than others. In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, as well as for practitioners in these areas. It can also be used as a textbook for graduate courses on risk bounds and model uncertainty.

Page 18 of 194