• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.165-170
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• 2004

This paper will derive explicit unified pricing formulas for eight types of outside barrier options, respectively. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity. The eight types of barrier options are up-and-in, up-and-out, down-and-in and down-and-out call (or put) options.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.207-220
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• 1999

In this paper, some of the issue about a group sequential method are considered in the Bayesian context. The continuous time optimal stopping boundary can be used to approximate the optimal stopping boundary for group sequential designs. The exact stopping boundary for group sequential design is obtained by using the backward induction method and is compared with the continuous optimal stopping boundary and the corrected continuous stopping boundary.

• Journal of Industrial Technology
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• v.2
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• pp.27-31
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• 1982

An approximation to the ARL for cusum control charts is derived using a Brownian motion approximation to the cumulative sum. The accuracy of this approximation is numerically evaluated and the results are compared with those obtained by other method.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.31-36
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• 2003

Using a short time expansion of the fundamental solution of heat equation by analysis of Wiener functional with the help of Malliavin calculus, we obtain the asymptotic expansion of the mean distance of Brownian motion on Riemannian manifolds.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.385-393
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• 2003

Let Y(t) be a stochastic integral process represented by Brownian motion. We show that YHt (t) is continuous in t with probability one for Molder function Ht of exponent ${\beta}$ and finally we derive asymptotic self-similar process YM (t) which converges to Yw (t).

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.327-334
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• 2000

Suppose that there is a population of hidden objects of which the total number N is unknown. From such data, we derive some properties of the limiting processes of stopping time in estimating a population size.

• Proceedings of the Korean Magnestics Society Conference
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• 2008.12a
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• pp.182.2-182.2
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• 2008

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1083-1101
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• 2022

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class 𝔻.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.187-200
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• 2013

In this paper, we deal with the problem of deciding a hedging volatility for ATM plain options when we hedge those options based on geometric Brownian motion. For this, we study the relation between hedging volatility and hedge profit&loss(P&L) as well as perform Monte Carlo simulations and real data analysis to examine how differently hedge P&L is affected by the selection of hedging volatility. In conclusion, using a relatively low hedging volatility is found to be more favorable for hedge P&L when underlying asset prices are expected to be range bound; however, a relatively high volatility is found to be favorable when underlying asset prices are expected to move on a trend.

• The Journal of Asian Finance, Economics and Business
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• v.1 no.4
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• pp.5-13
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• 2014

This study contributes to addressing the problem of an aging population by providing important information that determines feasible monthly payments for the clients of Chinese reverse mortgage products and by promoting the implementation of reverse mortgages in China. The variables used in this study include mean values obtained from time series data, of the rate of increase of housing prices, and the probability value, interest rate, and mortality rate obtained through the geometric Brownian motion (GBM). For mortality rates, China Life Insurance female mortality rates (2000-2003) were used. This study aims to apply the main variables that affect reverse mortgage products in a monthly payment model based on Chinese financial market conditions, and determine loan values. In this study, Shanghai's reverse mortgage monthly payments, by age levels, were calculated through the loan-to-value (LTV) and payment (PMT) methods to evaluate the value of the reverse mortgages. Based on the optimal combination of the three factors of payment amount, loan interest rates, and the level of acceptance of prices, efforts must be made to extract the best value for the elderly. Only in this way can the interests of both lenders and borrowers be protected, by increasing the market share and economies of scale of the reverse mortgage industry and effectively improving the living standards of the elderly.