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Mun-Chol Kim

Publications and source records attributed to Mun-Chol Kim.

11 recordsLinked to original sources
arXiv2019

Uniqueness, Comparison and Stability for Scalar BSDEs with {Lexp(μsqrt(2log(1+L)))}-integrable terminal values and monotonic generators

This paper considers a class of scalar backward stochastic differential equations (BSDEs) with $L\exp(μ\sqrt{2\log(1+L)})$-integrable terminal values. We associate these BSDEs with BSDEs with integrable parameters through Girsanov change. Using this technique, we prove uniqueness, comparisons and stability for them under an extended monotonicity condition (more precisely one sided Osgood condition).

math.PR↗
arXiv2019

A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration

In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard iteration but it differs on underlying Monte-Carlo sample generation and enables an improvement in the sense of complexity. We prove the explicit error estimates for the case where the generator does not depend on control variate.

math.NA↗
arXiv2018

A Stable Minutia Descriptor based on Gabor Wavelet and Linear Discriminant Analysis

The minutia descriptor which describes characteristics of minutia, plays a major role in fingerprint recognition. Typically, fingerprint recognition systems employ minutia descriptors to find potential correspondence between minutiae, and they use similarity between two minutia descriptors to calculate overall similarity between two fingerprint images. A good minutia descriptor can improve recognition accuracy of fingerprint recognition system and largely reduce comparing time. A good minutia descriptor should have high ability to distinguish between different minutiae and at the same time should be robust in difficult conditions including poor quality image and small size image. It also should be effective in computational cost of similarity among descriptors. In this paper, a robust minutia descriptor is constructed using Gabor wavelet and linear discriminant analysis. This minutia descriptor has high distinguishing ability, stability and simple comparing method. Experimental results on FVC2004 and FVC2006 databases show that the proposed minutia descriptor is very effective in fingerprint recognition.

cs.CV↗
arXiv2018

The Binomial Tree Method and Explicit Difference Schemes for American Options with Time Dependent Coefficients

Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partition of time interval with equal parts is used. A time interval partition method that allows binomial tree dynamics of the underlying asset's price is provided. Conditions under which the prices of American option by BTM and EDS have the monotonic property on time variable are found. Using convergence of EDS for variational inequality model of American options to viscosity solution the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied.

q-fin.PR↗
arXiv2018

Adapted $θ$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations

In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $θ$-scheme, we reduce truncation errors by taking $θ$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment.

math.NA↗
arXiv2018

A generalized scheme for BSDEs based on derivative approximation and its error estimates

In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stability and convergence order. We present a condition for the distribution of sample points to guarantee the convergence of the scheme.

math.NA↗
arXiv2018

An efficient third-order scheme for BSDEs based on nonequidistant difference scheme

In this paper we propose an efficient third-order numerical scheme for backward stochastic differential equations(BSDEs). We use 3-point Gauss-Hermite quadrature rule for approximation of the conditional expectation and avoid spatial interpolation by setting up a fully nested spatial grid and using the approximation of derivatives based on non-equidistant sample points. As a result, the overall computational complexity is reduced significantly. Several examples show that the proposed scheme is of third-order and very efficient.

math.NA↗
arXiv2017

Existence of smooth solutions of multi-term Caputo-type fractional differential equations

This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem.

math.CA↗