• 대한수학회보
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• 제56권5호
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• pp.1355-1376
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• 2019

We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.13-22
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• 2019

This paper presents a symbolic method for solving a boundary value problem with inhomogeneous Stieltjes boundary conditions over integro-differential algebras. The proposed symbolic method includes computing the Green's operator as well as the Green's function of the given problem. Examples are presented to illustrate the proposed symbolic method.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.673-697
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• 2020

In this paper, we introduce and study the structured essential approximate and defect pseudospectrum of closed, densely defined linear operators in a Banach space. Beside that, we discuss some results of stability and some properties of these essential pseudospectra. Finally, we will apply the results described above to investigate the essential approximate and defect pseudospectra of the following integro-differential transport operator.

• 충청수학회지
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• 제34권2호
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• pp.169-180
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• 2021

This paper investigates the time-inconsistent agent's optimal consumption and investment problem under inflation risk. The agents' discount factor is governed by hyperbolic discounting, which has a random time to change. We impose the inflation risk which plays a crucial role in long-term financial planning. We derive the semi-analytic solution to the problem of sophisticated agents when the time horizon is finite.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.545-558
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• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

• East Asian mathematical journal
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• 제40권5호
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• pp.527-549
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• 2024

In this paper we study the semilinear first order evolution problems of Volterra type with Lipschitz continuous nonlinearities. Using the variational formulation of problems due to Dautray and Lions [6], we have proved the fundamental results on existence, uniqueness and continuous dependence of solutions. Especially in the proof of the regularity we have used the double regularization method. Applications to nonlinear partial integro-differential equations are given.

• 대한기계학회논문집
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• 제14권6호
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• pp.1621-1628
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• 1990

본 연구에서는 많은 실질적인 시스템에서, 많은 양의 복합된 전도, 대류, 복 사의 열전달 현상이 동시에 일어나기 때문에 복합된 열전달 모드가 다같이 다루어져야 만 한다. Fig.1에서 보는 바와 같이 얇은 원형휜이 튜브 주위에 무수히 부착되어 있 으며, 휜과 튜브주위를 기체가 흐르고 있다. 휜과 휜, 휜과 튜브표면, 휜과 주위환 경, 튜브표면과 주위환경 사이에서 복사 열전달 상호교환이 충분히 다루어졌다. 전 도, 대류, 복사기 동시에 일어나는 열전달 방정식은 비선형 적분-미분 방정식(nonlin- ear integro-differential equation)으로 표현된다. 온도 분포도(temperature dist- ributions), 열전달량(heat transfer rates), 휜효율(fin efficiencies), 휜유효성(f- ineffectivenesses)등이 계산되어졌고, 무차원 형태로 도표에 결과들을 제시하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 춘계 학술대회논문집
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• pp.15-28
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• 1998

As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.

• Journal of the Korean Data and Information Science Society
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• 제24권1호
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• pp.1-12
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• 2013

본 논문에서는 잉여금이 양의 추세모수를 갖는 확산과정을 따라 움직이고, 두 가지 유형의 보험청구가 있는 리스크 모형을 소개한다. 두 유형의 보험청구 금액은 서로 독립이고, 각각 지수분포를 따른다고 가정한다. 유형 I의 보험청구는 잦은 빈도로 발생하지만 청구 금액은 적고, 유형 II의 보험청구는 상대적으로 드물게 발생하지만 청구 금액이 많다고 가정한다. 적미분 방정식을 세워 잉여금이 없어지는 파산확률을 구하고, 각 유형에 의한 파산확률과 확산과정에 의해 자연적으로 파산이 이루어지는 확률을 함께 구한다. 또한 예제를 통해 두 유형의 보험청구와 확산과정이 전체 파산확률에 미치는 영향을 수치적으로 비교 분석한다.