Chung-Ki Cho

Second-order accurate difference methods for a one-sex model of population dynamics

A first-order hyperbolic equation of age and time variables describes a one-sex model of population dynamics. The second-order finite difference method in the characteristic (age,time) direction is used to approximate simultaneously both the age distribution

Estimation of local volatilities in a generalized Black-Scholes model

u(x,t)

An efficient numerical parameter estimation scheme for the space-dependent dispersion coefficient of a solute transport equation in porous media

of the solution and the total population

Numerical Estimation of Diffusivity in a Nonhysteretic Infiltration Problem

P(t)

A New Approach for Numerical Identification of Optimal Exercise Curve

. Algorithms and error analysis are given for the second-order convergence rate.

An Efficient Parameter Estimation Technique for a Solute Transport Equation in Porous Media

This paper studies a parameter estimation problem for a generalized Black-Scholes equation, which is used for option pricing. In estimating the volatility function from a set of market observations, we use an implicit finite difference scheme. The function space parameter estimation convergence (FSPEC) is proved and numerical simulations were performed.

A new approach for numerical identification of free boundary

An efficient numerical parameter estimation scheme for the space-dependent dispersion coefficient of a solute transport equation in porous media is developed. It is based on an optimization scheme, a fast inverse Laplace transform, and the Galerkin method. The computational costs of the method developed are reduced significantly compared with those of conventional methods. The accuracy and efficiency of the method are shown through numerical experiments.

Dual-Mesh Characteristics for Particle-Mesh Methods for the Simulation of Convection-Dominated Flows

Nonhysteretic infiltration in nonswelling soil is modelled by a nonlinear convection- diffusion equation. A parameter estimation scheme for the spatially varying soil water diffusivity is developed and its convergence is proved. A numerical simulation is performed to show the theoretical results.

Parameter estimation approach to the free boundary for the pricing of an american call option

This paper deals with American put options, which is modelled by a free boundary problem for a nonhomogeneous generalized Black-Scholes equation. We present a parameter estimation technique to compute the put option price as well as the optimal exercise curve. The forward problem of computing the put option price with a given parameter of the function space for the free boundary employs the upwind finite difference scheme. The inverse problem of minimizing the cost functional over that function space uses the Levenberg-Marquardt method. Numerical experiments show that the approximation scheme satisfies appropriate convergence properties. Our method can be applied to the case that the volatility is a function of time and asset variables.

An essentially non-oscillatory Crank–Nicolson procedure for incompressible Navier–Stokes equations

Many parameter estimation problems arising in the solute transport equations in porous media involve numerous time integrations. An efficient adaptive numerical method is introduced in this paper. The method reduces the computational costs significantly compared with those of the conventional time-marching schemes due to the single time-integration, the spatial adaptiveness, and the O(log(N)) effects of the method, where N is the spatial approximation dimension. The efficiency and accuracy of the proposed algorithm is shown through a simple one-dimensional model. However, the methodology can be applied for more general multi-dimensional models.