• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.2
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• pp.45-57
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• 2004

The purpose of this paper is studying the valuation of option prices in Incomplete markets. A market is said to be incomplete if the given traded assets are insufficient to hedge a contingent claim. This situation occurs, for example, when the underlying stock process follows jump-diffusion processes. Due to the jump part, it is impossible to construct a hedging portfolio with stocks and riskless assets. Contrary to the case of a complete market in which only one equivalent martingale measure exists, there are infinite numbers of equivalent martingale measures in an incomplete market. Our research here is focusing on risk minimizing hedging strategy and its associated minimal martingale measure under the jump-diffusion processes. Based on this risk minimizing hedging strategy, we characterize the dynamics of a risky asset and derive the valuation formula for an option price. The main contribution of this paper is to obtain an analytical formula for a European option price under the jump-diffusion processes using the minimal martingale measure.

• Korean Journal of Applied Biomechanics
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• v.24 no.4
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• pp.385-390
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• 2014

The purpose of this study was to investigate the effects of landing tasks on the anterior cruciate ligament (ACL) injury risk factors in female basketball players. Fifteen female basketball players performed a drop landing and a drop landing with a vertical jump on the 40 cm height box. Three-dimensional motion analysis system and ground reaction force system was used for calculate the ACL injury risk factors. Paired samples t-test with Bonfferoni correction were performed. The drop landing with a vertical jump had the higher knee flexion angle, peak knee varus moment, trunk flexion angle than a drop landing. However, the drop landing had the higher trunk rotation angle than a drop landing with a vertical jump. These results indicate that seemingly minor variations between drop landing and drop landing with a vertical jump may influence the ACL injury risk factors. Caution should be used when comparing studies using different landing tasks.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.735-749
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• 2014

This paper studies the asymptotic behavior of the finite-time ruin probability in a jump-diffusion risk model with constant force of interest, upper tail asymptotically independent claims and a general counting arrival process. Particularly, if the claim inter-arrival times follow a certain dependence structure, the obtained result also covers the case of the infinite-time ruin probability.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.23-45
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• 2015

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1376
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• 2019

We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

• Journal of Korea Port Economic Association
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• v.34 no.1
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• pp.99-110
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• 2018

This study empirically examines simple methodology to quantify the risk resulted from the uncertainty of bunker price and foreign exchange rate, which cause main resources of the cost in shipping industry during the periods between $1^{st}$ of January 2010 and $31^{st}$ of January 2018. To shed light on the risk measurement in cash flows we tested GBM(Geometric Brownian Motion) frameworks such as the model with conditional heteroskedasticity and jump diffusion process. The main contribution based on empirical results are summarized as following three: first, the risk analysis, which is dependent on a single variable such as freight yield, is extended to analyze the effects of multiple factors such as bunker price and exchange rate return volatility. Second, at the individual firm level, the need for risk management in bunker price and exchange rate is presented as cash flow. Finally, based on the scale of the risk presented by the analysis results, the shipping companies are required that there is a need to consider what is appropriate as a means of risk management.

• Korean Journal of Applied Biomechanics
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• v.32 no.1
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• pp.9-16
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• 2022

Objective: The purpose of this study was to investigate how the chronic ankle instability affects postural control during forward jump landing. Method: 20 women with chronic ankle instability (age: 21.7 ± 1.6 yrs, height: 162.1 ± 3.7 cm, weight: 52.2 ± 5.8 kg) and 20 healthy adult women (age: 21.8 ± 1.6 yrs, height: 161.9 ± 4.4 cm, weight: 52.9 ± 7.2 kg) participated in this study. For the forward jump participants were instructed to stand on two legs at a distance of 40% of their body height from the center of force plate. Participants were jump forward over a 15 cm hurdle to the force plate and land on their non-dominant or affected leg. Kinetic and kinematic data were obtained using 8 motion capture cameras and 1 force plates and joint angle, vertical ground reaction force and center of pressure. All statistical analyses were using SPSS 25.0 program. The differences in variables between the two groups were compared through an independent sample t-test, and the significance level was to p < .05. Results: In the hip and knee joint angle, the CAI group showed a smaller flexion angle than the control group, and the knee joint valgus angle was significantly larger. In the case of ankle joint, the CAI group showed a large inversion angle at all events. In the kinetic variables, the vGRF was significantly greater in the CAI group than control group at IC and mGRF. In COP Y, the CAI group showed a lateral shifted center of pressure. Conclusion: Our results indicated that chronic ankle instability decreases the flexion angle of the hip and knee joint, increases the valgus angle of the knee joint, and increases the inversion angle of the ankle joint during landing. In addition, an increase in the maximum vertical ground reaction force and a lateral shifted center of pressure were observed. This suggests that chronic ankle instability increases the risk of non-contact knee injury as well as the risk of lateral ankle sprain during forward jump landing.

• The Korean Journal of Financial Management
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• v.25 no.2
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• pp.69-101
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• 2008

We empirically investigate the option leverage property that should be priced under much more general conditions than the Black-Scholes assumptions and the option redundancy property that is based on the assumption that the underlying asset price follows a one-dimensional diffusion process and examine the systematic risk factors implied in the return dynamics of KOSPI 200 index options. We find that the option leverage pattern is similar to the theoretical result but the options are not redundant securities and in the nonlinear structure of option payoffs, the traders of KOSPI 200 index options price the systematic higher-moments and the negative volatility risk premium significantly affects delta-hedged gains, even after accounting for jump fears. But the empirical evidence on jump risk preference is less conclusive.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1073-1086
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• 2009

This paper considers the problems of martingale measures and risk-minimizing hedging strategies in the market with restricted information. By constructing a general restricted information market model, the explicit relation of arbitrage and the minimal martingale measure between two different information markets are discussed. Also a link among all equivalent martingale measures under restricted information market is given. As an example of restricted information markets, this paper constitutes a jump-diffusion process model and presents a risk minimizing problem under different information. Through $It\hat{o}$ formula and projection results in Schweizer[13], the explicit optimal strategy for different market information are given.

• Korean Journal of Applied Biomechanics
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• v.23 no.3
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• pp.219-223
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• 2013

The purpose of the study was to investigate the effects of gymnasts shoes on risk factors of anterior cruciate ligament injuries during drop-landing followed by vertical jump in female gymnasts. Thirteen female gymnasts were recruited and performed randomly drop-landing followed by vertical jump in height of her knee with and without shoes. Kinematics and ground reaction data were collected to estimate the anterior cruciate ligament injuries risk factors. Data were analyzed with paired samples t-test with Bonferroni correction. Female gymnasts with shoes showed more reduced thigh maximum adduction angle, and knee maximum extension moment than without shoes. Female gymnasts with shoes showed more increased shank maximum abduction angle than without shoes. In conclusion, Female gymnasts with shoes reduced anterior cruciate ligament injuries risk factors.