교육개혁과 사범대학의 발전 과제

송성주 한국교원교육학회 1998 한국교원교육연구 Vol.15 No.1

Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression

송성주,Jaehong Jeong,송종우,김정훈 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.2

When the underlying asset price process follows a Lévy process, the market becomes incomplete, in which the option pricing can be a complicated problem. This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the option price as the expected value of the discounted payoff and expand it at the Black–Scholes price assuming that the price process converges weakly to the Black–Scholes model. The price can be approximated by a formula with 4 parameters, which can easily be estimated using option prices observed in the market. The proposed price explains the market option data better than the Black–Scholes price in real data application with KOSPI 200.

An Asymptotic Decomposition of Hedging Errors

송성주,Per A. Mykland 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.2

This paper studies the problem of option hedging when the underlyingasset price process is a compound Poisson process. By adopting an asymp-totic approach to let the security price converge to a continuous process, wend a closed-form hedging strategy that improves the classical Black-Scholeshedging strategy in a quadratic sense. We rst show that the scaled Black-Scholes hedging error has a limit in law, and that limit is decomposed intoa part that can be traded away and a part that is purely unreplicable. TheBlack-Scholes hedging strategy is then modied by adding the replicablepart of its hedging error and by adding the mean-variance hedging strategyto the nonreplicable part. Some results of simulation experiments are alsoprovided.AMS 2000 subject classications.Primary 91B28; Secondary 60F05.Keywords.Hedging error, compound Poisson processes, weak convergence.1. IntroductionPerfect hedging of an option is impossible in the real world. In a completenancial market, every contingent claim is exactly attainable by investing inthe market. But in most real instances, the market is not complete. Underthe classical Black-Scholes setting, in which the stock price process is a geometricBrownian motion, we can construct a perfect hedging strategy because their setupassures that the market is complete. However, the stock price process is not ageometric Brownian motion and even not continuous in reality. Stocks move inxed increments that are multiples of the tick size and sometimes there are alsoReceived December 2005; accepted May 2006.1Corresponding author. Department of Statistics, Purdue University, West Lafayette, IN47909-2067, USA (e-mail: ssong@stat.purdue.edu)

낙동강 하구생태계의 세균 생물량과 이차생산성

송성주,권오섭,이혜주,이진애,김영의,Song, Sung-Joo,Kwon, O-Seob,Lee, Hye-Joo,Lee, Jin-Ae,Kim, Young-Eui 한국미생물학회 1994 미생물학회지 Vol.32 No.3

부영양화된 낙동강 하구역에서 세균에 의한 용존 유기물의 이용능을 조사하고 이에 미치는 환경요인의 영향을 파악하기 위하여 미생물학적 요인과 물리화학적 환경요인의 연중 변화를 분석하였다. 총세균수는 0.33 ~ $2.09{\times}10^7$ cells/ml의 변화폭을 나타냈으며, 오염부하량이 큰 정점에서 종속영양세균의 개체수와 비례하였다. 세균이 체적과 생물량은 각각 0.064~0.156 ${\mu}m^3$/cell, 0.163~1.036 ${\mu}g$-C/ml을 나타냈다. 세균의 이차생산성은 0.24~60.86 ${\mu}g$-C/l/h의 범위로 측정되었으며, 부영양화 지표로 사용되는 환경인자와 밀접한 관계를 보였다. 담수역에 속하는 정점에서의 세균생산성의 계절별 변화는 동계에 최고치를, 하계에 최저치를 나타내어 갈수기의 오염부하량 증가와 밀접한 상관성을 보였다. 해수역에 속하는 다대의 경우 동계에 낮은 값을, 하계에 높은 값을 나타내고, 환경요인 중 엽록소 a, 수은 등과 밀접한 상관성을 보였다 (r>0.5, p<0.05). 이로 미루어 낙동강 하구의 하구언 상류역에서는 주위에서 유입되는 유기물이, 하구언 하류역에서는 식물성 플랑크톤의 광합성 산무링 세균의 이차생산성에 미치는 주 영양물질임을 암시하고 있다. To investigate the bacterial potentials for utilizing dissolved organic matter in highly eutrophic estuary, the annual fluctuations of microbiological and physicochemical environmental parameters were analyzed in Naktong River Estuary. Total bacterial number ranged from 0.33 to $2.09{\times}10^7$ cells/ml, and correlated with the heterotrophic bacterial numbers in more eutrophic sites, especially. Bacterial biovolume and biomass varied between 0.064 and 0.156 2.09${\mu}m^3$/cell, 0.163 and 1.036 ${\mu}g$-C/ml, respectively. Bacterial secondary productivity ranged from 0.24 to 60.86 ${\mu}g$-C/l/h, and showed high correlations with the environmental parameters of pollution indicator. The seasonal variation pattern of bacterial productivity in freshwater sites was high in winter and low in summer, which was interpreted as the results of pollution loads varied with the amount of rainfall. In seawater site, the pattern was different from those of freshwater sites; high in summer and low in winter. In this site, the values of bacterial productivity showed positive correaltions with chlorophyll a, heterotrophic bacterial number, and temperature (r>0.5, p<0.05). These results suggested that the main source of organic matter which influences the bacterial productivity may be allochthonous materials in the upper freshwater zone of Naktong River Barrage, and autochthonous algal excretory products in the lower seawater zone of Naktong River Barrage.

Asymptotic option price with bounded expected loss

송성주,송종우 한국통계학회 2008 Journal of the Korean Statistical Society Vol.37 No.4

This paper studies the problem of option pricing in an incomplete market, where the exact replication of an option may not be possible. In an incomplete market, we suppose a situation where a hedger wants to invest as little as possible at the beginning, but he/she wants to have the expected squared loss at the end not exceeding a certain constant. We study this problem when the log of the underlying asset price process is compound Poisson, which converges to a Brownian motion with drift. In the limit, we use the mean-variance approach to find a hedging strategy which minimizes the expected squared loss for a given initial investment. Then we find the asymptotic minimum investment with the expected squared loss bounded by a given upper bound. Some numerical results are also provided.

예측모형 잔차의 다변량 분포 적합을 통한 미세먼지 리스크 관리

송성주,조경상 한국보험법학회 2020 한국보험법학회 학술발표회 논문집 Vol.2020 No.2

한국형 실시간 내부미터링 평가를 위한 시뮬레이터 환경 개발

송성주,이승환,오영태,이상수 한국ITS학회 2003 한국ITS학회 학술대회 Vol.2003 No.1

Asymptotic Option Pricing under a Pure Jump Process

송성주 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.3

This paper studies the problem of option pricing in an incomplete market.The market incompleteness comes from the discontinuity of the underlyingasset price process which is, in particular, assumed to be a compound Poissonprocess. To nd a reasonable price for a European contingent claim, we rstnd the unique minimal martingale measure and get a price by taking anexpectation of the payo under this measure. To get a closed-form price, weuse an asymptotic expansion. In case where the minimal martingale measureis a signed measure, we use a sequence of martingale measures (probabilitymeasures) that converges to the equivalent martingale measure in the limitto compute the price. Again, we get a closed form of asymptotic option price.It is the Black-Scholes price and a correction term, when the distribution ofthe return process has nonzero skewness up to the rst order.

SaaS형 교통정보시스템 도입 필요성 및 발전방향

송성주 대한교통학회 2023 대한교통학회 학술대회지 Vol.89 No.-

미시적 시뮬레이터를 이용한 실시간 신호제어시스템(COSMOS) 평가 시뮬레이션 환경 개발

송성주,이승환,이상수 대한교통학회 2004 대한교통학회지 Vol.22 No.2

실시간 신호제어시스템은 현장의 교통정보를 수집하여 교통상황에 맞게 자동으로 신호제어를 수행하는 시스템이다. 그러나 현재까지 국내의 실시간 신호제어시스템인 COSMOS를 적절하게 모의실험 할 수 있는 미시적 시뮬레이터가 없는 실정이다. 따라서 본 연구에서는 세계적으로 널리 사용되고 있는 미시적 시뮬레이션 모형인 NETSIM모형을 기반으로 하여 COSMOS 시스템을 평가할 수 있도록 통합 시뮬레이션 환경을 개발하였다. 본 논문은 COSMOS 평가시뮬레이터의 모듈 중에서 모의 실험환경 내에서 차량의 이동에 따라 실시간으로 검지기정보를 추출해내는 모듈과 주요 신호변수 중 하나인 COSMOS 녹색현시배분알고리즘모듈을 제시하였다. 개발된 평가시뮬레이터 내의 정보흐름 정확성을 평가해본 결과, 연산과정 및 정보흐름이 정확한 것으로 확인되었다. 그리고 개발된 시뮬레이터를 개선하기 위한 향후과제들을 논문의 마지막에 제시하였다.