Asymptotic Approximations to CEV and SABR Models

Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β < 1, ρ = 0. We also compute large-time asymptotics for the constant elasticity of variance (CEV) model in the large-time, fixed-strike regime and a new large-time, large-strike regime, and for the uncorrelated CEV-Heston model. Finally, we translate these results into a large-time estimates for implied volatility using the recent work of Gao and Lee (2011) and Tehranchi (2009).

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equations in parametric space for cumulative probability functions. The generators are ultra-fast, very accurate and can be trained for any asset model described by stochastic differential equations. These are “single solve,” so they do not require retraining when parameters of the stochastic model are changed (e.g., recalibration of volatility). Once trained, the neural TDPF generators can be transferred to less powerful computers where they can be used for e.g. option pricing at speeds as fast as if the TPDF were known in a closed form. We illustrate the computational efficiency of the proposed neural approximations of TPDFs by inserting them into numerical option pricing methods. We demonstrate a wide range of applications including the Black-Scholes-Merton model, the standard Heston model, the SABR model, and jump-diffusion models. These numerical experiments confirm the ultra-fast speed and high accuracy of the developed neural TPDF generators. This paper was accepted by Kay Giesecke, finance. Funding: H. Su received research funding support from Nottingham Business School at Nottingham Trent University. M. V. Tretyakov was supported by the Engineering and Physical Sciences Research Council [Grant EP/X022617/1]. D. P. Newton received research funding support from the School of Management at Bath University. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.01448 .

<div class="htmlview paragraph">Electrical Computer Aided Engineering (CAE) is necessary and useful for the automotive industry [<span class="xref">1</span>,<span class="xref">2</span>]. It provides the user with necessary information that helps him/her make faster and more certain design decisions. CAE facilitates for the user options and the means to locate and choose optimums [<span class="xref">6</span>]. It requires models that best represent the actual system while avoiding unnecessary numerical overhead. Therefore, it is necessary to build the mathematical model in a systematic way that captures dynamics of the actual system [<span class="xref">3</span>]. Also, an optimal solution for the system parameters is required to increase the accuracy of the model and to make a correct decision while designing, testing, and validating [<span class="xref">3</span>,<span class="xref">6</span>]. This paper studies the CAE analysis of a PMDC motor. It develops a systematic approach to model, simulate and analyze PMDC motors with robust output. It enhances the accuracy of PMDC to a 6-Sigma level. A robust model minimizes the effort required in analyzing, predicting and validating the outcome of the motor. The uniqueness in this model is the use of Least Squares algorithm to solve for the optimal value of the motor parameters and the use for Recursive Least Squares (RLS) [<span class="xref">7</span> (page 70)] for On-Line learning. The use of learning overcomes a wide band of ambiguity and non-linearity included in the actual motor. The developed model introduces a procedure for calculating each of the motor parameters (e.g. R<sub>a</sub>, L<sub>a</sub>, K<sub>T</sub>, K<sub>v</sub>, J, D, T<sub>Loss</sub>). In this paper, simulation study uses a seat motor assembly that consists of three different motors as an example. The Saber simulator is used for running the simulation study. The actual data (experimental lab results) and the estimated data (Saber model) are then compared to assure the validity of the seat motor model compared to the physical seat motor.</div>

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation). The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field. The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12]. This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.

Regression Sensitivities for Initial Margin Calculations

In this paper an investigation is undertaken to explore the nature of the flow in the vicinity of the trailing edge of Joukowski-type airfoil configurations. Making use of the asymptotic interactive boundary layer theory, the basic flow profiles in the attached and detached flow regions are computed numerically through integrating the interactive boundary layer equations governing the flow motion for sufficiently large Reynolds numbers. Employing a Spectral Chebyshev collocation numerical integration scheme, boundary layer features corresponding to a number of thickness-to-chord ratio parameter cases are produced. The analysis carried out over the interaction region of the trailing edge shows that flow separation always takes place beyond certain critical value of the thickness-to-chord ratio parameter under the action of a self-induced pressure gradient. In addition, reversed flow regions of a sufficiently large size are found to be absolutely unstable, within the framework of linear spatio-temporal stability analysis in combination with the Briggs--Bers branch point criterion.

In this chapter, models of hydrocyclones will be ordered from a fluid dynamics perspective and an attempt will be made to present the velocity and pressure distribution inside the device. With experimental values of the velocity distributions, mass and linear momentum, equations were solved for the simplest inviscid approach combining a free vortex with a sink, rotational inviscid models, models based on the exact solution of the Reynolds equation for highly idealized conditions and solutions using different mathematical techniques such as asymptotic expansions, similarity solutions and boundary layer flows.

Asymptotic roof boundary layer solutions are obtained for the quasi‐linear seepage exclusion problem for elliptic‐cylindrical and spheroidal cavities of arbitrary aspect ratio h. The remarkably simple result for ϑmax, the maximum dimensionless potential at the cavity wall, is ϑmax(σ) ∼ 2σ + f0(h) + [f1(h)/σ] + ]f2(h)/σ2 + … where σ=½ αk−1 (α is sorptive number; k is apical total curvature) and the fn are polynomials in h−2 of degree (n + 1). The results agree, as they should, with previous results for the circular cylinder and sphere (h=1) and the parabolic cylinder and paraboloid (h=∞). Connections noted in earlier studies between apical sharpness and the variation of potential along the cavity wall are generalized and made quantitative. The singular (h =0) strip and disc are of especial interest: they indicate behavior near the critical upstream stagnation point on cavities (and impermeable obstacles) with flat strip‐ and disc‐shaped roofs but otherwise (within some limits) arbitrary. For the strip, ϑmax(S1) ∼ 4S12 + 9 ‐ (36/S12) + ⋯, and for the disc, ϑmax(S1) ∼ 2S12 + 6 ‐ (27/S12) + ⋯, where s1=½αl1 (l1 is semiwidth or radius). The central importance of ϑmax is that seepage water enters, or is excluded from, the cavity, depending on whether K0/K1 (K0 is downward steady seepage velocity far from the cavity; K1 is saturated hydraulic conductivity) exceeds or does not exceed ϑmax−1.

In this paper, we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group-valued field with a prescribed gauge transformation. As an illustration, we detail some examples. Two of them are based on known results: the first one provides a reinterpretation of the symmetry breaking mechanism of the electroweak part of the Standard Model of particle physics; the second one is an application to Einstein's theory of gravity described as a gauge theory in terms of Cartan connections. The last example depicts a new situation: starting with a gauge field theory on Atiyah Lie algebroids, the gauge invariant composite fields describe massive vector fields. Some mathematical and physical discussions illustrate and highlight the relevance and the generality of this approach.

Searches for new heavy resonances decaying into different pairings of $W$, $Z$, or Higgs bosons, as well as directly into leptons, are presented using a data sample corresponding to 36.1fb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 13 TeV collected during 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting bosonic decay modes in the $qqqq$, $\nu\nu qq$, $\ell\nu qq$, $\ell\ell qq$, $\ell\nu\ell\nu$, $\ell\ell\nu\nu$, $\ell\nu\ell\ell$, $\ell\ell\ell\ell$, $qqbb$, $\nu\nu bb$, $\ell\nu bb$, and $\ell\ell bb$ final states are combined, searching for a narrow-width resonance. Likewise, analyses selecting the leptonic $\ell\nu$ and $\ell\ell$ final states are also combined. These two sets of analyses are then further combined. No significant deviation from the Standard Model predictions is observed. Three benchmark models are tested: a model predicting the existence of a new heavy scalar singlet, a simplified model predicting a heavy vector-boson triplet, and a bulk Randall-Sundrum model with a heavy spin-2 Kaluza-Klein excitation of the graviton. Cross-section limits are set at the 95% confidence level using an asymptotic approximation and are compared with predictions for the benchmark models. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The data exclude a heavy vector-boson triplet with mass below 5.5 TeV in a weakly coupled scenario and 4.5 TeV in a strongly coupled scenario, as well as a Kaluza-Klein graviton with mass below 2.3 TeV.

A uniform asymptotics of the surface Love modes for a special case of anisotropy (tranverse isotropy) of an elastic media is obtained. In constructing the asymptotics of surface waves, the space-time (ST) ray method is employed. The wave field of each Love mode is represented as the sum of the ST caustic expansion involving the Airy functions with a real eikonal and two correction terms that are ST ray solutions, which in fact are inhomogeneous waves with complex eikonals. The eikonals and coefficients of the caustic and ray series are sought in the form of expansions in powers of two variables. The first variable is the distance from the surface, whereas the other characterizes the proximity of the caustic of a ray field to the boundary surface. Thanks to the specific structure of the elasticity tensor for a transversely isotropic medium, the boundary surface is necessarily a plane. A recursion process of computation of higher terms of the asymptotic expansion allows one to trace the conversion of the formulas obtained to the known ray solutions for isotropic elastic media. Relations between the elasticity parameters of a medium are obtained that ensure the existence of SH Love waves in a transversely isotropic medium and that are consistent with the conditions of the positiveness of the elastic energy of deformation. Bibliography: 6 titles.

On Existence and Uniqueness of Equilibrium in Noisy Rational Expectations Economies

Preparation of respirable nanoparticle agglomerates of the low melting and ductile drug ibuprofen: Impact of formulation parameters

The problems associated with formulating and validating mathematical models for describing and predicting human target acquisition response are considered. In particular, the extension of the human observer model to include the acquisition phase as well as the tracking segment is presented. Relationship of the Observer model structure to the more complex Standard Optimal Control model formulation and to the simpler Transfer Function/Noise representation is discussed. Problems pertinent to structural identifiability and the form of the parameterization are elucidated. A systematic approach toward the identification of the observer acquisition model parameters from ensemble tracking error data is presented.

An integrated energy system, referred to specifically as a heterogeneous energy system that combines cooling, heating, power, etc., is a dynamic system containing continuous as well as discrete behaviors on both technical and economic levels. Currently, the comprehensive utilization of multiple forms of energy and the implementation of the energy market have made the simulation of such a system very complicated, which is reflected in two aspects. First, the simulation model becomes complex and varied. Second, the time-varying characteristics of the models are quite diverse. Therefore, a standard and normative modeling and simulation method is urgently needed. This work aims to obtain a compatible modeling and simulation method for the energy economy coupling system. The individual-based model is widely used to describe organisms in an ecology system that are similar to the energy–economy coupled system. Inspired by this, a general simulation approach based on the individual-based model is proposed in this paper to overcome these existing problems. The standard formal expression model is built, then its structure and elements explained in detail, and multi-scale time simulation supported to model and simulate an integrated energy system that is coupled with markets. In addition, a simulator is designed and implemented based on multi-agent framework and model-view-controller architecture. Finally, a simulation case of a conceived scenario was designed and executed, and the results analysis proved the validity and versatility of the proposed approach. The proposed method has the advantages of model standardization, multi-scale time compatibility, distributed simulation capability, and privacy protection. These advantages support and strengthen each other. Through these studies, a systematic approach was formed that could improve the standardization of modeling and simulation in the energy–economy research area.