• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.395-404
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• 2012

Our first aim of this paper is to define maximal operators a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ${\leq}$ a < $\infty$ by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.269-277
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• 2008

Let $f=(f_n)$ be a nonnegative submartingale such that ${\parallel}f{\parallel}{\infty}{\leq}1\;and\;g=(g_n)$ be a martingale, adapted to the same filtration, satisfying $${\mid}d_{gn}{\mid}{\leq}{\mid}df_n{\mid},\;n=0,\;1,\;2,\;....$$ The paper contains the proof of the sharp inequality $$\limits^{sup}_ n\;\mathbb{E}{\Phi}({\mid}g_n{\mid}){\leq}{\Phi}(1)$$ for a class of convex increasing functions ${\Phi}\;on\;[0,\;{\infty}]$, satisfying certain growth condition. As an application, we show a continuous-time version for stochastic integrals and a related estimate for smooth functions on Euclidean domain.

• 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.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.75-89
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• 1996

This paper proposes a goodness-of-fit test for checking the adequacy of the additive risk model with a binary covariate. The test statistic is based on martingale residuals, which is the extended form of Wei(1984)'s test. The proposed test is shown to be consistent and asymptotically normally distributed under the regularity conditions. Furthermore, the test procedure is illustrated with two set of real data and the results are discussed.

• Korea Journal of Hospital Management
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• v.11 no.3
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• pp.19-41
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• 2006

The Objective of this study was to design the model which predict the future cash flow of hospitals and on the basis of designed model to support sound hospital management by the prediction of future cash flow. The five cash flow measurement variables discussed in financial accrual part were used as variables and these variables were defined as NI, NIDPR, CFO, CFAI, CC. To measure the cash flow B/S related variables, P/L related variables and financial ratio related variables were utilized in this study. To measure cash flow models were designed and to estimate the prediction ability of five cash flow models, the martingale model and the market model were utilized. To estimate relative prediction outcome of cash flow prediction model and simple market model, MAE and MER were used to compare and analyze relative prediction ability of the cash flow model and the market model and to prove superiority of the model of the cash flow prediction model, 32 Regional Public Hospital's cross-section data and 4 year time series data were combined and pooled cross-sectional time series regression model was used for GLS-analysis. To analyze this data, Firstly, each cash flow prediction model, martingale model and market model were made and MAE and MER were estimated. Secondly difference-test was conducted to find the difference between MAE and MER of cash flow prediction model. Thirdly after ranking by size the prediction of cash flow model, martingale model and market model, Friedman-test was evaluated to find prediction ability. The results of this study were as follows: when t-test was conducted to find prediction ability among each model, the error of prediction of cash flow model was smaller than that of martingale and market model, and the difference of prediction error cash flow was significant, so cash flow model was analyzed as excellent compare with other models. This research results can be considered conductive in that present the suitable prediction model of future cash flow to the hospital. This research can provide valuable information in policy-making of hospital's policy decision. This research provide effects as follows; (1) the research is useful to estimate the benefit of hospital, solvency and capital supply ability for substitution of fixed equipment. (2) the research is useful to estimate hospital's liqudity, solvency and financial ability. (3) the research is useful to estimate evaluation ability in hospital management. Furthermore, the research should be continued by sampling all hospitals and constructed advanced cash flow model in dimension, established type and continued by studying unified model which is related each cash flow model.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.691-701
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• 2012

In this note, we define the It$\hat{o}$ integral with respect to analogue of Wiener process and investigate its various properties and examples.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.619-631
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• 2000

We study a class of catalytic super Brownian motion X in 1-dimension. We show under some conditions of catalyst, the process X is absolutely continuous and we get a stochastic partial differential equation for X.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.551-558
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• 2006

We establish a weak law of large numbers for sequence of random elements with values in p-uniformly smooth Banach space. Our result is more general and stronger than some well-known ones.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.451-458
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• 1998

Problem of testing linearity among general class of first order nonlinear time series models is discussed. The null hypotheses of linearity is identified via conditional expectations. A consistent test is then suggested and relevant limiting results are derived. It is worth indicating that any specific alternatives are not specified.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.301-306
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• 2018

I obtain the optimal portfolio and consumption strategies of an investor who have a Cobb-Douglas utility function. And I assume that there is negative wealth constraints. This constraints mean that the investor can borrow partially against her future labor income.