• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.505-512
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• 2017

In this paper, we explain how the exact closed-form solutions of the classical problems of viscous fluid flow over a heated stretching plate and shrinking sheet can be obtained by a reliable method.

• 대한수학회보
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• 제42권2호
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• pp.231-244
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• 2005

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

• 대한수학회보
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• 제44권4호
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Journal of the Korean Statistical Society
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• 제14권1호
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• pp.18-28
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• 1985

Optimal screening procedures for improving outgoing product quality based on correlated normal variables are presented. The performance variable and the screening variables are assumed to be jointly normally distributed. These procedures do not require specialized tables, and closed-form solutions are obtained for the case of one-sided specification. Methods for finding optimal solutions for the case of two-sided specifications are also considered.

• 충청수학회지
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• 제27권1호
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• pp.145-149
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• 2014

I consider the optimal consumption and portfolio selection problem with nonnegative wealth constraints using the dynamic programming approach. I use the constant relative risk aversion (CRRA) utility function and disutility to derive the closed-form solutions.

• 충청수학회지
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• 제27권2호
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• pp.219-225
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• 2014

I use the dynamic programming approach to study the optimal consumption and investment problem with regime-switching and constant labor income. I derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility and constant disutility.

• 충청수학회지
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• 제29권2호
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• pp.329-336
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• 2016

The optimal portfolio choice problem with a stochastic income is considered in continuous-time framework. We provide a novel approach to treat the stochastic income when the market is complete. The developed method is useful to obtain closed-form solutions of the problems under borrowing constraints.

• 충청수학회지
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• 제26권3호
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• pp.571-576
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• 2013

In this paper, we solve the optimal investment problem when the investor gets labor income and may have a wage increase. We assume the investor has constant absolute risk aversion(CARA) utility and obtain closed form solutions.

• 충청수학회지
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• 제25권2호
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• pp.277-281
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• 2012

I study an optimal consumption and portfolio selection problem with regime-switching using a dynamic programming method. With constant relative risk aversion (CRRA) utility I obtain optimal solutions in closed-form.

• 충청수학회지
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• 제31권1호
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• pp.65-73
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• 2018

We investigate the optimal consumption and investment problem of working agent who faces tax system on consumption, labor income, savings and investment. By applying martingale method, we obtain the closed-form solutions so it is possible to verify the effect of tax system analytically.