• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.145-151
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• 1992

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.659-673
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• 1998

In this paper we consider a security market whose asset price process is a vector semimartingale. The market is said to be fair if there exists an equivalent martingale measure for the price process, deflated by a numeraire asset. It is shown that the fairness of a market is invariant under the change of numeraire. As a consequence, we show that the characterization of the fairness of a market is reduced to the case where the deflated price process is bounded. In the latter case a theorem of Kreps (1981) has already solved the problem. By using a theorem of Delbaen and Schachermayer (1994) we obtain an intrinsic characterization of the fairness of a market, which is more intuitive than Kreps' theorem. It is shown that the arbitrage pricing of replicatable contingent claims is independent of the choice of numeraire and equivalent martingale measure. A sufficient condition for the fairness of a market, modeled by an Ito process, is given.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.185-193
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• 1996

In this paper we consider the gambler's ruin problem with N players and derive the formula for computing the expected ruin time when the initial fortunes of all N players are the same. And we present an example for the case of N = 5.

• 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.

• 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.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.117-130
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• 1997

We study the asymptotic behavior of the maximum partial likelihood estimator in the Cox proportional hazards model in the presence of nuisance parameters when the entry of patients is staggered. When entry of patients is simultaneous and there is only one regression parameter in the Cox model, the efficient score process of the partial likelihood is martingale and converges weakly to a time-chnaged Brownian motion. Our problem is to get a similar result in the presence of nuisance parameters when entry of patient is staggered.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.135-138
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• 2005

In this paper, we consider the problem of testing for parameter change in time series models based on a cusum of squares. Although the test procedure is well-established for the mean and variance in time series models, a general parameter case was not discussed in literatures. Therefore, here we develop the cusum of squares type test for parameter change in a more general framework. As an example, we consider the change of the parameters in an RCA(1) model. Simulation results are reported for illustration.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.397-404
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• 2005

In this note, we characterize the limiting diffusion of a diploid model by defining the discrete generator for the resealed Markov chain. We conclude that this limiting diffusion model is with uncountable state space and mutation selection and special 'mutation or gene conversion rate'.

• Proceedings of the Korean Statistical Society Conference
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• 2001.11a
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• pp.185-189
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• 2001

In this paper, we consider the problem of testing for parameter changes in time series models based on a sequential test. Although the test procedure is well-established for the mean and variance change, a general parameter case has not been discussed in the literature. Therefore, we develop a sequential test for parameter changes in a more general framework.