• 충청수학회지
• /
• 제34권2호
• /
• pp.169-180
• /
• 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.

• 대한수학회논문집
• /
• 제18권3호
• /
• pp.569-580
• /
• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

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

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

• Structural Engineering and Mechanics
• /
• 제38권5호
• /
• pp.593-618
• /
• 2011

This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler's medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.

• 한국대기환경학회지
• /
• 제14권4호
• /
• pp.303-312
• /
• 1998

To obtain the solution to the time-dependent particle size distribution of an aerosol undergoing gravitational coagulation, the moment method was used which converts the non linear integro-differential equation to a set of ordinary differential equations. A semi-numerical solution was obtained using this method. Subsequently, an analytic solution was given by approximating the collision kernel into a form suitable for the analysis. The results show that during gravitational coagulation, the geometric standard deviation increases and the geometric mean radius decreases as time increases.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1033-1047
• /
• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제6권2호
• /
• pp.9-24
• /
• 2002

Total Variation(TV) regularization method is effective for reconstructing "blocky", discontinuous images from contaminated image with noise. But TV is represented by highly nonlinear integro-differential equation that is hard to solve. There have been much effort to obtain stable and fast methods. C. Vogel introduced "the Fixed Point Lagged Diffusivity Iteration", which solves the nonlinear equation by linearizing. In this paper, we apply multigrid(MG) method for cell centered finite difference (CCFD) to solve system arise at each step of this fixed point iteration. In numerical simulation, we test various images varying noises and regularization parameter $\alpha$ and smoothness $\beta$ which appear in TV method. Numerical tests show that the parameter ${\beta}$ does not affect the solution if it is sufficiently small. We compute optimal $\alpha$ that minimizes the error with respect to $L^2$ norm and $H^1$ norm and compare reconstructed images.

• 대한기계학회논문집
• /
• 제19권11호
• /
• pp.2995-3002
• /
• 1995

The cooling problem of the hot internal pipe flow has been investigated. Simultaneous conduction, convection, and radiation were considered with azimuthally varying convective heat loss at the pipe wall. A complex, nonlinear integro-differential radiative transfer equation was solved by the discrete ordinates method (or called S$_{N}$ method). The energy equation was solved by control volume based finite difference technique. A parametric study was performed by varying the conduction-to-radiation parameter, optical thickness, and scattering albedo. The results have shown that initially the radiatively active medium could be more efficiently cooled down compared with the cases otherwise. But even for the case with dominant radiation, as the medium temperature was lowered, the contribution of conduction became to exceed that of radiation.n.

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