Abstract: This paper studies the optimal investment strategies for a plan member (PM) in a defined contribution (DC) pension scheme with transaction cost, taxes on invested funds and couple risky assets (stocks) under the Ornstein-Uhlenbeck (O-U) process. The PM’s portfolio is assumed to consist of a risk-free asset and two risky assets where the two risky assets are driven by the O-U process. The Legendre transformation and dual theory is use to transform the resultant optimal control problem which is a nonlinear partial differential equation (PDE) into linear PDE and the resultant linear PDE is then solved for the explicit solutions of the optimal investment strategies for PM exhibiting constant absolute risk aversion (CARA) using change of variable technique. Furthermore, theoretical analysis is used to study the influences of some sensitive parameters on the optimal investment strategies with observations that the optimal investment strategies for the two risky assets increase with increase in the dividend and decreases with increase in tax on the invested funds, risk averse coefficient, initial fund size and the transaction cost.
Abstract: An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.
Abstract: In this paper, we have investigated the nonlinear
time-fractional hyperbolic partial differential equation (PDE) for
its symmetries and invariance properties. With the application of
this method, we have tried to reduce it to time-fractional ordinary
differential equation (ODE) which has been further studied for exact
solutions.
Abstract: This paper presents an analytical method to solve
governing consolidation parabolic partial differential equation (PDE)
for inelastic porous Medium (soil) with consideration of variation of
equation coefficient under cyclic loading. Since under cyclic loads,
soil skeleton parameters change, this would introduce variable
coefficient of parabolic PDE. Classical theory would not rationalize
consolidation phenomenon in such condition. In this research, a
method based on time space mapping to a virtual time space along
with superimposing rule is employed to solve consolidation of
inelastic soils in cyclic condition. Changes of consolidation
coefficient applied in solution by modification of loading and
unloading duration by introducing virtual time. Mapping function is
calculated based on consolidation partial differential equation results.
Based on superimposing rule a set of continuous static loads in
specified times used instead of cyclic load. A set of laboratory
consolidation tests under cyclic load along with numerical
calculations were performed in order to verify the presented method.
Numerical solution and laboratory tests results showed accuracy of
presented method.
Abstract: CEMTool is a command style design and analyzing
package for scientific and technological algorithm and a matrix based
computation language. In this paper, we present new 2D & 3D
finite element method (FEM) packages for CEMTool. We discuss
the detailed structures and the important features of pre-processor,
solver, and post-processor of CEMTool 2D & 3D FEM packages. In
contrast to the existing MATLAB PDE Toolbox, our proposed FEM
packages can deal with the combination of the reserved words. Also,
we can control the mesh in a very effective way. With the introduction
of new mesh generation algorithm and fast solving technique, our
FEM packages can guarantee the shorter computational time than
MATLAB PDE Toolbox. Consequently, with our new FEM packages,
we can overcome some disadvantages or limitations of the existing
MATLAB PDE Toolbox.