Australian Mathematical Society (AustMS): E-Journals
Not a member yet
3379 research outputs found
Sort by
Mean-variance equilibrium asset-liability management strategy with cointegrated assets
No full textThis paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability is random and cannot be fully financed or hedged through the financial market. For mean–variance investors, an additional concern is the rational time-consistency issue, which ensures that a decision made in the future will not be restricted by the current surplus level. By putting all these factors together, this paper derives a closed-form feedback equilibrium control for time-consistent mean–variance asset-liability management problems with cointegrated risky assets. The solution is built upon the Hamilton–Jacobi–Bellman framework addressing time inconsistency.
doi: 10.1017/S144618112000016
Distribution of the divisor function at consecutive integers
No full textIn this paper we sharpen Hildebrand’s earlier result on a conjecture of Erdos on limit points of the sequence {d(n)/d(n + 1)
Pricing timer options: second-order multiscale stochastic volatility asymptotics
No full textWe 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 options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated.
doi:10.1017/S144618112100024
Localized radial basis functions for no-arbitrage pricing of options under stochastic alpha–beta–rho dynamics
No full textClosed-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 problem for long-term maturities by numerically solving the no-arbitrage partial differential equation with an absorbing boundary condition at zero. Localized radial basis functions in a finite-difference mode are employed for the development of a computational method for solving the resulting two-dimensional pricing equation. The proposed method can use either multiquadrics or inverse multiquadrics, which are shown to have comparable performances. Numerical results illustrate the accuracy of the proposed method and, more importantly, that the computed risk-neutral probability densities are nonnegative. These two key properties indicate that the method of solution using localized meshless methods is a viable and efficient means for price computations under SABR dynamics.
doi:10.1017/S144618112100023
A note on the axisymmetric diffusion equation
No full textWe 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 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.
doi:10.1017/S144618112100011
Adaptive grid refinement using the generalised finite difference method
No full textThe combination of the Generalised Finite Difference Method (GFDM), and adaptive grid refinement is applied to solve 2D
fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new Computational Fluid Dynamics (CFD) formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers. To verify the accuracy of this combnation, analytical 2D and 3D Laplace partial differential equations (PDE's) are solved by two methods. The first method uses the Finite Difference Method (FDM) over a uniform grid of nodes, and the second method uses the GFDM over a
non-uniform grid of nodes. Computational cost and accuracy comparisons are made for both methods
Conformal image registration based on constrained optimization
No full textImage registration is the process of finding an alignment between two or more images so that their appearances match. It has been widely studied and applied to several fields, including medical imaging and biology, where it is related to morphometrics. In this paper, we present a construction of conformal diffeomorphisms which is based on constrained optimization. We consider a set of different penalty terms that aim to enforce conformality, based on discretizations of the Cauchy–Riemann equations and geometric principles, and demonstrate them experimentally on a variety of images.
doi:10.1017/S144618112000022
On existence and uniqueness of solutions to a pantograph type equation
No full textWe show existence and uniqueness of solutions to an initial boundary value problem that entails a pantograph type functional partial differential equation with two advanced nonlocal terms. The problem models cell growth and division into two daughter cells of different sizes. There is a paucity of information about the solution to the problem for an arbitrary initial cell distribution.
doi:10.1017/S144618112100002
Distribution of integers with prescribed structure and applications
No full texthttp://dx.doi.org/10.1017/S000497271200033