• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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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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• v.14 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.85-90
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• 2013

We use the dynamic programming method to investigate the optimal consumption and investment problem with regime-switching. We derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility.