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APPROXIMATE PRICING OF DERIVATIVES UNDER FRACTIONAL STOCHASTIC VOLATILITY MODEL ANZIAM J. (IF 0.9) Pub Date : 2024-03-12 Y. HAN, X. ZHENG
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
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ACTIVE REMODELLING OF TISSUES TO DESCRIBE BIPHASIC RHEOLOGICAL RESPONSES ANZIAM J. (IF 0.9) Pub Date : 2024-02-26 DOMENIC P. J. GERMANO, STEPHANIE KHUU, ADRIANNE L. JENNER, JAMES M. OSBORNE, MARY R. MYERSCOUGH, MARK B. FLEGG
Tissues form from collections of cells that interact together mechanically via cell-to-cell adhesion, mediated by transmembrane cell adhesion molecules. Under a sufficiently large amount of induced stress, these tissues can undergo elastic deformation in the direction of tension, where they then elongate without any topological changes, and experience plastic deformation within the tissue. In this
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NONLINEAR SELF-MODULATION OF GRAVITY-CAPILLARY WAVES ON SHEAR CURRENTS IN FINITE DEPTH ANZIAM J. (IF 0.9) Pub Date : 2024-01-12 TANMOY PAL, ASOKE KUMAR DHAR
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
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ON MODELLING WATER QUALITY WITH STOCHASTIC DIFFERENTIAL EQUATIONS ANZIAM J. (IF 0.9) Pub Date : 2024-01-09 MAHMOUD B. A. MANSOUR
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
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THE METRIC OPERATORS FOR PSEUDO-HERMITIAN HAMILTONIAN ANZIAM J. (IF 0.9) Pub Date : 2023-10-23 WEN-HUA WANG, ZHENG-LI CHEN, WEI LI
The Hamiltonian of a conventional quantum system is Hermitian, which ensures real spectra of the Hamiltonian and unitary evolution of the system. However, real spectra are just the necessary conditions for a Hamiltonian to be Hermitian. In this paper, we discuss the metric operators for pseudo-Hermitian Hamiltonian which is similar to its adjoint. We first present some properties of the metric operators
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AN IMEX-BASED APPROACH FOR THE PRICING OF EQUITY WARRANTS UNDER FRACTIONAL BROWNIAN MOTION MODELS ANZIAM J. (IF 0.9) Pub Date : 2023-09-07 WENTING CHEN, XIAOYING JIANG
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
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NUMERICAL ANALYSIS OF APPARATUS-INDUCED DISPERSION FOR DENSITY-DEPENDENT SOLUTE TRANSPORT IN POROUS MEDIA ANZIAM J. (IF 0.9) Pub Date : 2023-08-31 H. ZHANG, D. A. BARRY, B. SEYMOUR, G. HOCKING
The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data were analysed. The model simulations confirmed that flow nonuniformities induced by the apparatus are dissipated within the column when the distance
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WALL STABILIZATION IN MINES BY SPRAY-ON LINERS ANZIAM J. (IF 0.9) Pub Date : 2023-08-31 D. P. MASON, N. D. FOWKES, R. M. YEMATA, C. A ONYEAGOZIRI, H. YILMAZ
Thin spray-on liners (TSLs) have been found to be effective for structurally supporting the walls of mining tunnels and thus reducing the occurrence of rock bursts, an effect primarily due to the penetration of cracks by the liner. Surface tension effects are thus important. However, TSLs are also used to simply stabilize rock surfaces, for example, to prevent rock fall, and in this context crack penetration
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NOVEL STABILITY CONDITIONS FOR SOME GENERALIZATION OF NICHOLSON’S BLOWFLIES MODEL WITH STOCHASTIC PERTURBATIONS ANZIAM J. (IF 0.9) Pub Date : 2023-08-23 LEONID SHAIKHET, SYED ABBAS
We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained
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NUMERICAL SIMULATIONS FOR LARGELY DEFORMED BEAMS AND RINGS ADOPTING A NONTENSILE SMOOTHED PARTICLE HYDRODYNAMICS ALGORITHM ANZIAM J. (IF 0.9) Pub Date : 2023-08-15 THIEN TRAN-DUC, MICHAEL H. MEYLAN, NGAMTA THAMWATTANA
Three typical elastic problems, including beam bending, truss extension and compression, and two-rings collision are simulated with smoothed particle hydrodynamics (SPH) using Lagrangian and Eulerian algorithms. A contact-force model for elastic collisions and equation of state for pressure arising in colliding elastic bodies are also analytically derived. Numerical validations, on using the corresponding
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BURSTING SOLUTIONS OF THE RÖSSLER EQUATIONS ANZIAM J. (IF 0.9) Pub Date : 2023-08-10 A. C. FOWLER, M. J. MCGUINNESS
We provide an analytic solution of the Rössler equations based on the asymptotic limit $c\to \infty $ and we show in this limit that the solution takes the form of multiple pulses, similar to “burst” firing of neurons. We are able to derive an approximate Poincaré map for the solutions, which compares reasonably with a numerically derived map.
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THE ROLE OF THE MATHEMATICAL SCIENCES IN SUPPORTING THE COVID-19 RESPONSE IN AUSTRALIA AND NEW ZEALAND ANZIAM J. (IF 0.9) Pub Date : 2023-07-31 JAMES M. MCCAW, MICHAEL J. PLANK
Mathematical modelling has been used to support the response to the COVID-19 pandemic in countries around the world including Australia and New Zealand. Both these countries have followed similar pandemic response strategies, using a combination of strict border measures and community interventions to minimize infection rates until high vaccine coverage was achieved. This required a different set of
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AN EXAMINATION OF THE “LANIER WING” DESIGN ANZIAM J. (IF 0.9) Pub Date : 2023-07-21 Y. M. STOKES, W. L. SWEATMAN, G. C. HOCKING
Six patents were secured by E. H. Lanier from 1930 to 1933 for aeroplane designs that were intended to be exceptionally stable. A feature of five of these was a flow-induced “vacuum chamber” which was thought to provide superior stability and increased lift compared to typical wing designs. Initially, this chamber was in the fuselage, but later designs placed it in the wing by replacing a section of
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DOUBLE LAYERED COMPRESSIBLE MASKS ANZIAM J. (IF 0.9) Pub Date : 2023-07-17 N. D. FOWKES, D. P. MASON
Double-masking may be used to reduce the transmission of a virus. If additionally the masks are compressible, with different permeabilities and behaviour under compression, then it may be possible to design a mask that allows for easy breathing under normal breathing conditions, but is relatively impermeable under coughing or sneezing conditions. Such a mask could be both comfortable to wear and effective
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EXACT SOLUTIONS OF HYPERBOLIC REACTION-DIFFUSION EQUATIONS IN TWO DIMENSIONS ANZIAM J. (IF 0.9) Pub Date : 2023-07-17 P. BROADBRIDGE, J. GOARD
Exact solutions are constructed for a class of nonlinear hyperbolic reaction-diffusion equations in two-space dimensions. Reduction of variables and subsequent solutions follow from a special nonclassical symmetry that uncovers a conditionally integrable system, equivalent to the linear Helmholtz equation. The hyperbolicity is commonly associated with a speed limit due to a delay, $\tau $, between
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FLIGHT LIMITATIONS IMPOSED ON SINGLE ROTOR AND COAXIAL HELICOPTERS BY THE LIFT EQUATION ANZIAM J. (IF 0.9) Pub Date : 2023-07-17 B. MALDON, MICHAEL H. MEYLAN
To compute the maximum speed threshold for helicopters, we model the lift produced by the rotor blades. Using this model, we derive limits for each method traditionally used to alleviate dissymmetry of lift. Additionally, we find the minimum rotor angular velocity required to produce a prescribed lift at a given forward velocity. We derive conditions on the coefficient of lift for helicopter airfoils
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MODELLING MICROWAVES IN BAUXITE ANZIAM J. (IF 0.9) Pub Date : 2023-07-04 LATA I. PAEA, SIONE PAEA, MARK J. MCGUINNESS
Sending microwaves through bauxite ore allows almost continuous measurement of moisture content during offload by conveyor belt from a ship. Data and results from a microwave analyser were brought to a European Study Group with Industry at the University of Limerick, with the over-arching question of whether the results are accurate enough. The analyser equipment uses linear regression against phase
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ON THE SAFE STORAGE OF BAGASSE ANZIAM J. (IF 0.9) Pub Date : 2023-06-23 S. L. MITCHELL, T. G. MYERS
In this paper, we investigate the thermal evolution in a one-dimensional bagasse stockpile. The mathematical model involves four unknowns: the temperature, oxygen content, liquid water content and water vapour content. We first nondimensionalize the model to identify dominant terms and so simplify the system. We then calculate solutions for the approximate and full system. It is shown that under certain
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COUETTE FLOW OVER A HEAT ISLAND ANZIAM J. (IF 0.9) Pub Date : 2023-06-05 LAWRENCE K. FORBES, STEPHEN J. WALTERS
A viscous fluid is confined between two smooth horizontal walls, in a vertical channel. The upper wall may move with constant speed, but the lower wall is stationary and a portion of it is heated. A plume of heated fluid develops, and may also be swept downstream by the motion of the upper wall. When the heating effect is small and the upper plate does not move, a closed-form solution for the temperature
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A MODIFICATION TO THE SCHRÖDINGER EQUATION FOR BROADER BANDWIDTH GRAVITY-CAPILLARY WAVES ON DEEP WATER WITH DEPTH-UNIFORM CURRENT ANZIAM J. (IF 0.9) Pub Date : 2023-03-03 SOURAV HALDER, ASOKE KUMAR DHAR
We derive a nonlinear Schrödinger equation for the propagation of the three-dimensional broader bandwidth gravity-capillary waves including the effect of depth-uniform current. In this derivation, the restriction of narrow bandwidth constraint is extended, so that this equation will be more appropriate for application to a realistic sea wave spectrum. From this equation, an instability condition is
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A LOCAL PROJECTION STABILIZATION FOR CONVECTION–DIFFUSION–REACTION EQUATIONS USING BIORTHOGONAL SYSTEMS ANZIAM J. (IF 0.9) Pub Date : 2023-02-20 BISHNU P. LAMICHHANE, JORDAN A. SHAW-CARMODY
We consider a local projection stabilization based on biorthogonal systems for convection–diffusion–reaction differential equations with mixed boundary conditions. The approach based on biorthogonal systems is numerically more efficient than other existing approaches to obtain a uniform approximation for convection dominated problems. We prove optimal a priori error estimates for the proposed numerical
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A COMPARISON OF EXPLICIT RUNGE–KUTTA METHODS ANZIAM J. (IF 0.9) Pub Date : 2022-10-19 STEPHEN J. WALTERS, ROSS J. TURNER, LAWRENCE K. FORBES
Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two
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VOLATILITY SWAPS VALUATION UNDER A MODIFIED RISK-NEUTRALIZED HESTON MODEL WITH A STOCHASTIC LONG-RUN VARIANCE LEVEL ANZIAM J. (IF 0.9) Pub Date : 2022-09-26 XIN-JIANG HE, SHA LIN
We consider the pricing of discretely sampled volatility swaps under a modified Heston model, whose risk-neutralized volatility process contains a stochastic long-run variance level. We derive an analytical forward characteristic function under this model, which has never been presented in the literature before. Based on this, we further obtain an analytical pricing formula for volatility swaps which
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HIGH ORDER EXPLICIT SECOND DERIVATIVE METHODS WITH STRONG STABILITY PROPERTIES BASED ON TAYLOR SERIES CONDITIONS ANZIAM J. (IF 0.9) Pub Date : 2022-09-23 A. MORADI, A. ABDI, G. HOJJATI
When faced with the task of solving hyperbolic partial differential equations (PDEs), high order, strong stability-preserving (SSP) time integration methods are often needed to ensure preservation of the nonlinear strong stability properties of spatial discretizations. Among such methods, SSP second derivative time-stepping schemes have been recently introduced and used for evolving hyperbolic PDEs
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ON MULTIFRACTIONALITY OF SPHERICAL RANDOM FIELDS WITH COSMOLOGICAL APPLICATIONS ANZIAM J. (IF 0.9) Pub Date : 2022-08-18 PHILIP BROADBRIDGE, RAVINDI NANAYAKKARA, ANDRIY OLENKO
This paper investigates spatial data on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying mathematical model of the cosmic microwave background (CMB) data. We discuss the generalized multifractional Brownian motion and its pointwise Hölder exponent on the sphere. The multifractional approach is used to investigate the CMB data from the Planck mission
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BRANCHING TECHNIQUE FOR A BI-OBJECTIVE TWO-STAGE ASSIGNMENT PROBLEM ANZIAM J. (IF 0.9) Pub Date : 2022-08-15 EKTA JAIN, KALPANA DAHIYA, VANITA VERMA
We discuss a bi-objective two-stage assignment problem (BiTSAP) that aims at minimizing two objective functions: one comprising a nonlinear cost function defined explicitly in terms of assignment variables and the other a total completion time. A two-stage assignment problem deals with the optimal allocation of n jobs to n agents in two stages, where $n_1$ out of n jobs are primary jobs which constitute
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Improving the accuracy of retrieved cardiac electrical conductivities. ANZIAM J. (IF 0.9) Pub Date : 2022-08-12 A Kamalakkanna,P R Johnston,B M Johnston
Accurate values for the six cardiac conductivities of the bidomain model are crucial for meaningful electrophysiological simulations of cardiac tissue and are yet to be achieved. A two-stage optimisation process is used to retrieve the cardiac conductivities from cardiac potentials measured on a multi-electrode array-the first stage simultaneously fits all six conductivities, and the second stage fits
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FULLY 3D FLUID OUTFLOW FROM A SPHERICAL SOURCE ANZIAM J. (IF 0.9) Pub Date : 2022-08-10 LAWRENCE K. FORBES, STEPHEN J. WALTERS
We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories
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THE MAGIC OF NASH SOCIAL WELFARE IN OPTIMIZATION: DO NOT SUM, JUST MULTIPLY! ANZIAM J. (IF 0.9) Pub Date : 2022-07-07 HADI CHARKHGARD, KIMIA KESHANIAN, RASUL ESMAEILBEIGI, PARISA CHARKHGARD
We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective
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AN ANALYTICAL APPROXIMATION FOR CONVERTIBLE BONDS ANZIAM J. (IF 0.9) Pub Date : 2022-06-20 JOANNA GOARD
This paper looks at adapting the method of Medvedev and Scaillet for pricing short-term American options to evaluate short-term convertible bonds. However unlike their method, we provide explicit formulae for the coefficients of our series solution. This means that we do not need to solve complicated recursive systems, and can efficiently provide fast solutions. We also compare the method with numerical
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DISPERSAL OF HYDROGEN IN THE RETINA—A THREE-LAYER MODEL ANZIAM J. (IF 0.9) Pub Date : 2022-05-10 W. F. MANSOOR, G. C. HOCKING, D. E. FARROW
Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent
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THREE-DIMENSIONAL ANALYTICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION FOR AIR POLLUTION DISPERSION ANZIAM J. (IF 0.9) Pub Date : 2022-04-26 M. FARHANE, O. ALEHYANE, O. SOUHAR
We develop a new analytical solution of a three-dimensional atmospheric pollutant dispersion. The main idea is to subdivide vertically the planetary boundary layer into sub-layers, where the wind speed and eddy diffusivity assume average values for each sub-layer. Basically, the model is assessed and validated using data obtained from the Copenhagen diffusion and Prairie Grass experiments. Our findings
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EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ANZIAM J. (IF 0.9) Pub Date : 2022-04-25 P. RAMAZANI, A. ABDI, G. HOJJATI, A. MORADI
The paper deals with the construction of explicit Nordsieck second derivative general linear methods with s stages of order p with $p=s$ and high stage order $q=p$ with inherent Runge–Kutta or quadratic stability properties. Satisfying the order and stage order conditions together with inherent stability conditions leads to methods with some free parameters, which will be used to obtain methods with
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HOPF BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER HOLLING–TANNER PREDATOR-PREY MODEL WITH TIME DELAY ANZIAM J. (IF 0.9) Pub Date : 2022-04-05 C. CELIK, K. DEGERLİ
We study a fractional-order delayed predator-prey model with Holling–Tanner-type functional response. Mainly, by choosing the delay time $\tau $ as the bifurcation parameter, we show that Hopf bifurcation can occur as the delay time $\tau $ passes some critical values. The local stability of a positive equilibrium and the existence of the Hopf bifurcations are established, and numerical simulations
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STATIONARY MARKOVIAN ARRIVAL PROCESSES: RESULTS AND OPEN PROBLEMS ANZIAM J. (IF 0.9) Pub Date : 2022-02-22 AZAM ASANJARANI, YONI NAZARATHY
We consider two classes of irreducible Markovian arrival processes specified by the matrices C and D: the Markov-modulated Poisson process (MMPP) and the Markov-switched Poisson process (MSPP). The former exhibits a diagonal matrix D while the latter exhibits a diagonal matrix C. For these two classes we consider the following four statements: (I) the counting process is overdispersed; (II) the hazard
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DO POOR ENVIRONMENTAL CONDITIONS DRIVE TRACHOMA TRANSMISSION IN BURUNDI? A MATHEMATICAL MODELLING STUDY ANZIAM J. (IF 0.9) Pub Date : 2021-11-22 D. NDISABIYE, E. K. WATERS, R. GORE, H. SIDHU
Trachoma is an infectious disease and it is the leading cause of preventable blindness worldwide. To achieve its elimination, the World Health Organization set a goal of reducing the prevalence in endemic areas to less than $5$ % by 2020, utilizing the SAFE (surgery, antibiotics, facial cleanliness, environmental improvement) strategy. However, in Burundi, trachoma prevalences of greater than $5$ %
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NUMERICAL SOLUTIONS TO A FRACTIONAL DIFFUSION EQUATION USED IN MODELLING DYE-SENSITIZED SOLAR CELLS ANZIAM J. (IF 0.9) Pub Date : 2021-11-16 BENJAMIN MALDON, BISHNU PRASAD LAMICHHANE, NGAMTA THAMWATTANA
Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between
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A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS ANZIAM J. (IF 0.9) Pub Date : 2021-11-09 P. ASSARI, F. ASADI-MEHREGAN, M. DEHGHAN
The main goal of this paper is to solve a class of Darboux problems by converting them into the two-dimensional nonlinear Volterra integral equation of the second kind. The scheme approximates the solution of these integral equations using the discrete Galerkin method together with local radial basis functions, which use a small set of data instead of all points in the solution domain. We also employ
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BOUNDS ON THE CRITICAL TIMES FOR THE GENERAL FISHER–KPP EQUATION ANZIAM J. (IF 0.9) Pub Date : 2021-11-02 MARIANITO R. RODRIGO
The Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) equation is one of the prototypical reaction–diffusion equations and is encountered in many areas, primarily in population dynamics. An important consideration for the phenomena modelled by diffusion equations is the length of the diffusive process. In this paper, three definitions of the critical time are given, and bounds are obtained by a careful
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IDEAL PLANAR FLUID FLOW OVER A SUBMERGED OBSTACLE: REVIEW AND EXTENSION ANZIAM J. (IF 0.9) Pub Date : 2021-10-25 LAWRENCE K. FORBES, STEPHEN J. WALTERS, GRAEME C. HOCKING
A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent
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INTERACTION OF A SINGULAR SURFACE WITH A STRONG SHOCK IN THE INTERSTELLAR GAS CLOUDS ANZIAM J. (IF 0.9) Pub Date : 2021-09-23 J. JENA, S. MITTAL
We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface
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A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS ANZIAM J. (IF 0.9) Pub Date : 2021-09-23 LIAM C. MORROW, TIMOTHY J. MORONEY, MICHAEL C. DALLASTON, SCOTT W. MCCUE
The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to
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ALGORITHM TO CONSTRUCT INTEGRO SPLINES ANZIAM J. (IF 0.9) Pub Date : 2021-09-13 R. MIJIDDORJ, T. ZHANLAV
We study some properties of integro splines. Using these properties, we design an algorithm to construct splines $S_{m+1}(x)$ of neighbouring degrees to the given spline $S_m(x)$ with degree m. A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time
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ON OPTIMAL THRESHOLDS FOR PAIRS TRADING IN A ONE-DIMENSIONAL DIFFUSION MODEL ANZIAM J. (IF 0.9) Pub Date : 2021-09-07 MASAAKI FUKASAWA, HITOMI MAEDA, JUN SEKINE
We study the static maximization of long-term averaged profit, when optimal preset thresholds are determined to describe a pairs trading strategy in a general one-dimensional ergodic diffusion model of a stochastic spread process. An explicit formula for the expected value of a certain first passage time is given, which is used to derive a simple equation for determining the optimal thresholds. Asymptotic
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AN ANALYTICAL APPROXIMATION FORMULA FOR THE PRICING OF CREDIT DEFAULT SWAPS WITH REGIME SWITCHING ANZIAM J. (IF 0.9) Pub Date : 2021-09-02 XIN-JIANG HE, SHA LIN
We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure:
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SPECTRALLY ACCURATE OPTION PRICING UNDER THE TIME-FRACTIONAL BLACK–SCHOLES MODEL ANZIAM J. (IF 0.9) Pub Date : 2021-08-25 GERALDINE TOUR, NAWDHA THAKOOR, DÉSIRÉ YANNICK TANGMAN
We propose a Legendre–Laguerre spectral approximation to price the European and double barrier options in the time-fractional framework. By choosing an appropriate basis function, the spectral discretization is used for the approximation of the spatial derivatives of the time-fractional Black–Scholes equation. For the time discretization, we consider the popular $L1$ finite difference approximation
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AN ANALYTICAL OPTION PRICING FORMULA FOR MEAN-REVERTING ASSET WITH TIME-DEPENDENT PARAMETER ANZIAM J. (IF 0.9) Pub Date : 2021-08-23 P. NONSOONG, K. MEKCHAY, S. RUJIVAN
We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows
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PRICING TIMER OPTIONS: SECOND-ORDER MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS ANZIAM J. (IF 0.9) Pub Date : 2021-08-23 XUHUI WANG, SHENG-JHIH WU, XINGYE YUE
We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer
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FINITE MATURITY AMERICAN-STYLE STOCK LOANS WITH REGIME-SWITCHING VOLATILITY ANZIAM J. (IF 0.9) Pub Date : 2021-08-19 XIAOPING LU, ENDAH R. M. PUTRI
We study finite maturity American-style stock loans under a two-state regime-switching economy. We present a thorough semi-analytic discussion of the optimal redeeming prices, the values and the fair service fees of the stock loans, under the assumption that the volatility of the underlying is in a state of uncertainty. Numerical experiments are carried out to show the effects of the volatility regimes
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LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS ANZIAM J. (IF 0.9) Pub Date : 2021-08-19 N. THAKOOR
Closed-form explicit formulas for implied Black–Scholes volatilities provide a rapid evaluation method for European options under the popular stochastic alpha–beta–rho (SABR) model. However, it is well known that computed prices using the implied volatilities are only accurate for short-term maturities, but, for longer maturities, a more accurate method is required. This work addresses this accuracy
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OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL ANZIAM J. (IF 0.9) Pub Date : 2021-08-13 Y. HAN, Z. LI, C. LIU
We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution
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A NOTE ON THE AXISYMMETRIC DIFFUSION EQUATION ANZIAM J. (IF 0.9) Pub Date : 2021-07-21 ALEXANDER E. PATKOWSKI
We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for $u(r,t)$ as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.
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OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS ANZIAM J. (IF 0.9) Pub Date : 2021-07-21 CAIBIN ZHANG, ZHIBIN LIANG, KAM CHUEN YUEN
We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of
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ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH ANZIAM J. (IF 0.9) Pub Date : 2021-06-04 A. A. ZAIDI, B. VAN BRUNT
An advanced pantograph-type partial differential equation, supplemented with initial and boundary conditions, arises in a model of asymmetric cell division. Methods for solving such problems are limited owing to functional (nonlocal) terms. The separation of variables entails an eigenvalue problem that involves a nonlocal ordinary differential equation. We discuss plausible eigenvalues that may yield
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ANALYSIS OF CELL TRANSMISSION MODEL FOR TRAFFIC FLOW SIMULATION WITH APPLICATION TO NETWORK TRAFFIC ANZIAM J. (IF 0.9) Pub Date : 2021-05-18 A. S. MAULANA, S. R. PUDJAPRASETYA
The cell transmission model (CTM) is a macroscopic model that describes the dynamics of traffic flow over time and space. The effectiveness and accuracy of the CTM are discussed in this paper. First, the CTM formula is recognized as a finite-volume discretization of the kinematic traffic model with a trapezoidal flux function. To validate the constructed scheme, the simulation of shock waves and rarefaction
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SLOW-BURNING INSTABILITIES OF DUFORT–FRANKEL FINITE DIFFERENCING ANZIAM J. (IF 0.9) Pub Date : 2021-04-30 DAVID GALLOWAY, DAVID IVERS
DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety
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EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS ANZIAM J. (IF 0.9) Pub Date : 2021-04-29 B. F. AKERS, D. M. AMBROSE
We present an efficient, accurate computational method for a coordinate-free model of flame front propagation of Frankel and Sivashinsky. This model allows for overturned flames fronts, in contrast to weakly nonlinear models such as the Kuramoto–Sivashinsky equation. The numerical procedure adapts the method of Hou, Lowengrub and Shelley, derived for vortex sheets, to this model. The result is a nonstiff
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STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH ANZIAM J. (IF 0.9) Pub Date : 2021-04-19 ZUOXUN LI, KAI ZHANG
A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered
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EDITORIAL: SPECIAL ISSUE ON FINANCIAL MATHEMATICS AND QUANTITATIVE FINANCE ANZIAM J. (IF 0.9) Pub Date : 2021-04-01 SONG-PING ZHU,XIAOPING LU,XIN-JIANG HE
The nexus between world financial markets and the discipline of quantitative finance, which is heavily based on mathematics and statistics, has become increasingly clearer as a result of enormously expanded global financial derivative markets over the past two decades. To understand important and yet complicated market behaviours, mathematicians and statisticians worldwide have proposed many stochastic
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ESTIMATES FOR APPROXIMATE SOLUTIONS TO A FUNCTIONAL DIFFERENTIAL EQUATION MODEL OF CELL DIVISION ANZIAM J. (IF 0.9) Pub Date : 2021-03-12 STEPHEN TAYLOR, XUESHAN YANG
The functional partial differential equation (FPDE) for cell division, $$ \begin{align*} &\frac{\partial}{\partial t}n(x,t) +\frac{\partial}{\partial x}(g(x,t)n(x,t))\\ &\quad = -(b(x,t)+\mu(x,t))n(x,t)+b(\alpha x,t)\alpha n(\alpha x,t)+b(\beta x,t)\beta n(\beta x,t), \end{align*} $$is not amenable to analytical solution techniques, despite being closely related to the first-order partial differential