8 papers
American condor contracts with a cash component: A variational inequality approach
Kiyuob Jung, Jehan Oh, Namgwang Woo
We study a jointly exercised American condor contract whose payoff is a call condor payoff plus a positive cash amount. Its plateau and positive tails produce two inner exercise bo…
The specular ellipse method for scalar ordinary differential equations: exactness and accuracy up to fourth order
Kiyuob Jung
This paper introduces a family of one-step implicit methods for solving scalar ordinary differential equations. At each step, the update uses a scaled angular mean of two vector-fi…
Specular gradient methods for nonsmooth convex optimization in Euclidean spaces: a subgradient selection strategy
Kiyuob Jung
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradient…
Specular differentiation in normed vector spaces
Kiyuob Jung
This paper develops specular differentiation for mappings between real normed vector spaces, extending the classical notions of Gâteaux and Fréchet differentiability. These notions…
Specular differentiation in one dimension: a quasi-mean value theorem, regularity, and discontinuities
Kiyuob Jung
We develop a theory of specular differentiation on real intervals. The specular derivative is defined by averaging the angles associated with the forward and backward difference qu…
Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence
Kiyuob Jung, Jehan Oh
We propose the specular gradient method for one-dimensional convex optimization. Assuming that the minimum is attained and a suitable initial distance bound holds, we establish R-l…
The wave equation with specular derivatives
Kiyuob Jung, Jehan Oh
In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduc…
Regular specular differentiation in Euclidean spaces
Kiyuob Jung, Jehan Oh
We study the regular specular derivative, a generalized derivative defined at every point where both one-sided derivatives exist and are finite. Geometrically, it is the slope of t…