• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.677-683
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• 2012

W.Choi([1]) obtains a complete description of ergodic property and several property by making use of the semigroup method. In this note, we shall consider separately the martingale problems for two operators A and B as a detail decomposition of operator L. A key point is that the (K, L, $p$)-martingale problem in population genetics model is related to diffusion processes, so we begin with some a priori estimates and we shall show existence of contraction semigroup {$T_t$} associated with decomposition operator A.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.415-423
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• 2004

In allelic model X = ($x_1,\;x_2,...x_{d}$), $M_f(t)$= f(p(t)) - ${{\int}^{t}}_0$Lf(p(t))ds is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show uniqueness of martingale problem associated with mean vector and obtain a complete description of ergodic property by using of the semigroup method.

• East Asian mathematical journal
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• v.34 no.3
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• pp.331-338
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• 2018

We investigate the optimal consumption and portfolio strategies of an agent who has a constant elasticity of substitution (CES) utility function under the negative wealth constraint. We use the martingale method to derive the closed-form solution, and we give some numerical implications.

• 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 Korean Society for Industrial and Applied Mathematics
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• v.17 no.2
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• pp.115-128
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• 2013

The optimal portfolio selection problem under inflation risk and subsistence constraints is considered. There are index bonds to invest in financial market and it helps to hedge the inflation risk. By applying the martingale method, the optimal consumption rate and the optimal portfolios are obtained explicitly. Furthermore, the quantitative effect of inflation risk and subsistence constraints on the optimal polices are also described.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.103-112
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• 2020

This paper investigates the portfolio selection problem with flexible labor choice and stochastic income flow where the unit wage flow is governed by a stochastic process. The agent optimally chooses consumption, investment, and labor supply. We derive the closed-form solution by applying a martingale method even with the stochastic income flow.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.343-349
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• 2013

The optimal portfolio selection problem under inflation risk is considered in this paper. There are three assets the economic agent can invest, which are a risk free bond, an index bond and a risky asset. By applying the martingale method, the optimal consumption rate and the optimal portfolios for each asset are obtained explicitly.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.433-444
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• 1996

In contrast to the multiplicative risk model, the additive risk model specifies that the hazard function with covariates is the sum of, rather than product of, the baseline hazard function and the regression function of covariates. We, in this paper, propose a method for checking the adequacy of the additive risk model based on partial-sum of matingale residuals. Under the assumed model, the asymptotic properties of the proposed test statistic and approximation method to find the critical values of the limiting distribution are studied. Several real examples are illustrated.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.377-385
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• 2007

In this paper, by the equations of Mao [9] and Peng [5], we use the martingale method to establish the comparison theorems of backward stochastic differential equations (BSDEs). We generalize the results of Cao-Yan [1].