• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.705-714
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• 2002

We consider a jump-diffusion model generated by a Levy process for an asset price. We present an error estimate for the option prices between the jump-diffusion model and the Black-scholes model when the former converges weakly to the latter.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.837-845
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• 1998

In this work, we consider Euler approxiamtion for one-dimensional jump-diffusion processes under Yamada-Watanabe type conditions on the coefficients which turns out to converge to the strong solution in uniform $L^1$-sense.

• 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.

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.4
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• pp.249-253
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• 2012

This paper suggests a numerical method for valuation of American options under the Kou model (double exponential jump diffusion model). The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the conventional numerical method, the finite difference method for PIDE (partial integro-differential equation).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.43-50
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• 2014

In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.

• 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.

• 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.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• Journal of the Korean Magnetic Resonance Society
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• v.13 no.1
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• pp.35-55
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• 2009

The two correlation times previously obtained in our coupled $^{13}C$ relaxation measurement for the methyl group in 2,6-dichlorotoluene may be used as a criterion for evaluating the reorientation dynamics of an internal rotor. We numerically tested an extended diffusion model and the Smoluchowski diffusion equation to see how the rotational inertial effect and jump character contribute to the internal correlation time ratio of the internal rotor. We also analytically solved the general jump model with three different rate constants in a sixfold symmetric potential barrier. By assuming that the internal rotation of the methyl group in 2,6-dichlorotoluene can be described in terms of jumps among sixfold harmonic potential wells, we can conclude that the jump model satisfactorily reproduce the experimental data and the rate for sixfold jump is at least 1.53 times as great as that of a threefold jump.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.163-177
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• 2016

We consider a jump diffusion process for high-frequency financial asset data. We apply the stationary bootstrapping to construct a bootstrap test for jumps. First-order asymptotic validity is established for the stationary bootstrapping of the jump ratio test under the null hypothesis of no jump. Consistency of the stationary bootstrap test is proved under the alternative of jumps. A Monte-Carlo experiment shows the advantage of a stationary bootstrapping test over the test based on the normal asymptotic theory. The proposed bootstrap test is applied to construct continuous-jump decomposition of the daily realized variance of the KOSPI for the year 2008 of the world-wide financial crisis.