• Journal of Applied and Pure Mathematics
• /
• v.4 no.5_6
• /
• pp.287-297
• /
• 2022

In this paper, we consider a risk-minimization hedging problem for a special European contingent claims. The existence and uniqueness of strategy are given constructively. Firstly, a non-standard European contingent is demonstrated as stochastic payment streams. Then the existence of the risk minimization strategy and also the uniqueness are proved under two kinds market information by using Galtchouk-Kunita-Watanabe decomposition and constructing a 0-achieving strategy risk-minimizing strategies in full information. And further, we have proven risk-minimizing strategies exists and is unique under restrict information by constructing a weakly mean-selffinancing strategy.

• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.51-62
• /
• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.575-585
• /
• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.43-61
• /
• 2020

We extend the work of A. Beauville on rank 2 vector bundles on a smooth curve in several directions. We give families of examples with large dimension, add new existence and non-existence results and prove the existence of indecomposable limits with arbitrary rank. To construct the large dimensional families we use the examples of limits of rank 2 trivial bundles on ℙ² and ℙ³ due to C. Banica. We also consider a more flexible notion: limits of trivial bundles on nearby curves.

• Journal of Integrative Natural Science
• /
• v.6 no.3
• /
• pp.181-182
• /
• 2013

In this note, we are concerned with a class of semi-linear elliptic pdes with exponential nonlinearity in a bounded domain. Here, the nonlinearity is more or less growing exponentially with power p. We consider the problem under two types of Dirichlet boundary condition. We give existence and non-existence of solutions for those problems and some asymptotics.

• Journal of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1261-1277
• /
• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.33-45
• /
• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.

• Kyungpook Mathematical Journal
• /
• v.21 no.1
• /
• pp.71-74
• /
• 1981

In this paper a general third order differential equation encountered in the flow of fluids in general and hopefully elsewhere. Sufficient conditions for existence & uniqueness of its solutions are given.

• East Asian mathematical journal
• /
• v.32 no.5
• /
• pp.621-633
• /
• 2016

We establish the existence of positive solutions to nonlocal boundary value problems with integral boundary condition and non-negative real boundary parameter by mainly using the Schauder-Fixed point theorem.

• Journal of the Chungcheong Mathematical Society
• /
• v.5 no.1
• /
• pp.143-149
• /
• 1992

The purpose of this note is to give a new existence theorem of equilibrium in non-compact generalized games with uncountable number of agents.