Browsing by Author "Sheu, Yuan-Chung"

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A Generalized Renewal Equation for Perturbed Compound Poisson Processes with Two-Sided Jumps
(2009)
Chen, Yu-Ting
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where only downward jumps are allowed.
A note on first passage functionals for hyper-exponential jump-diffusion processes
(2013-01-04)
Chen, Yu-Ting
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Sheu, Yuan-Chung
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Chang, Ming-Chi
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應用數學系
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Department of Applied Mathematics
This investigation concerns the hyper-exponential jump-diffusion processes. Following the exposition of the two-sided exit problem by Kyprianou [10] and Asmussen and Albrecher [1], this study investigates first passage functionals for these processes. The corresponding boundary value problems are solved to obtain an explicit formula for the first passage functionals.
A NOTE ON R-BALAYAGES OF MATRIX-EXPONENTIAL LEVY PROCESSES
(2009-04-21)
Chen, Yu-Ting
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
In this note we give semi-explicit solutions for r-balayages of matrix-exponential Levy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by Mordecki in [11], Asmussen, Avram and Pistorius in [3], Chen, Lee and Sheu in [7], and many others.
AN INTEGRAL-EQUATION APPROACH FOR DEFAULTABLE BOND PRICES WITH APPLICATION TO CREDIT SPREADS
(2009-03-01)
Chen, Yu-Ting
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Lee, Cheng-Few
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
We study defaultable bond prices in the Black-Cox model with jumps in the asset value. The jump-size distribution is arbitrary, and following Longstaff and Schwartz (1995) and Zhou (2001) we assume that, if default occurs, the recovery at maturity depends on the,severity of default'. Under this general setting, the vehicle for our analysis is an integral equation. With the aid of this, we prove some properties of the bond price which are consistent numerically and empirically with earlier works. In particular, the limiting credit spread as time to maturity tends to 0 is nonzero. As a by product, we show that the integral equation implies an infinite-series expansion for the bond price.
An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model
(2007-07-01)
Chen, Yu-Ting
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Lee, Cheng-Few
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Sheu, Yuan-Chung
;
應用數學系
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資訊管理與財務金融系註：原資管所+財金所
Under the assumption that the asset value follows a phase-type jump-diffusion, we show that the expected discounted penalty satisfies an ODE and obtain a general form for the expected discounted penalty. In particular, if only downward jumps are allowed, we get an explicit formula in terms of the penalty function and jump distribution. On the other band, if the downward jump distribution is a mixture of exponential distributions (and upward jumps are determined by a general Levy measure), we obtain closed-form solutions for the expected discounted penalty. As an application, we work out an example in Leland's structural model with jumps. For earlier and related results, see Gerber and Landry [Insur. Math. Econ. 22:263276, 1998], Hilberink and Rogers [Finance Stoch. 6:237-263, 2002], Asmussen et al. [Stoch. Proc. Appl. 109:79-111, 2004], and Kyprianou and Surya [Finance Stoch. 11:131-152, 2007].
Diffuse to fuse EEG spectra - Intrinsic geometry of sleep dynamics for classification
(2020-01-01)
Liu, Gi-Ren
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Lo, Yu-Lun
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Malik, John
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Sheu, Yuan-Chung
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Wu, Hau-Tieng
We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information from two electroencephalograms (EEG). The diffusion geometry approach helps organize the nonlinear dynamical structure hidden in the EEG signal. The visualization is achieved by the nonlinear dimension reduction capability of the chosen diffusion geometry algorithms. For the automatic annotation purpose, the support vector machine is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC* (SC = Sleep Cassette) and ST* (ST = Sleep Telemetry), with the leave-one-subject-out cross validation. When we have a single EEG channel (Fpz-Cz), the overall accuracy, macro F1 and Cohen's kappa achieve 82.72%, 75.91% and 76.1% respectively in Sleep-EDF SC* and 78.63%, 73.58% and 69.48% in Sleep-EDF ST*. This performance is compatible with the state-of-the-art results. When we have two EEG channels (Fpz-Cz and Pz-Oz), the overall accuracy, macro F1 and Cohen's kappa achieve 84.44%, 78.25% and 78.36% respectively in Sleep-EDF SC* and 79.05%, 74.73% and 70.31% in Sleep-EDF ST*. The results suggest the potential of the proposed algorithm in practical applications. (C) 2019 Elsevier Ltd. All rights reserved.
Disorder Chaos in the Spherical Mean-Field Model
(2015-07-01)
Chen, Wei-Kuo
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Hsieh, Hsi-Wei
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Hwang, Chii-Ruey
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Sheu, Yuan-Chung
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應用數學系
We study the problem of disorder chaos in the spherical mean-field model. It concerns the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra\'s replica symmetry breaking scheme, we establish this at the levels of the free energy and the Gibbs measure.
First exit from an open set for a matrix-exponential Levy process
(2017-08-01)
Chen, Yu-Ting
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Chen, Yu-Tzu
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
We study the first exit from a general open set for a one-dimensional Levy process, where the Levy measure is proportional to a two-sided matrix-exponential distribution. Under appropriate conditions on the Levy measure, we obtain an explicit solution for the joint distribution of the first-exit time and the position of the Levy process upon first exit, in terms of the zeros and poles of the corresponding Laplace exponent. The present result complements several earlier works on the use of exit sets for Levy processes with algebraically similar Laplace exponents, where exits from open intervals are the main focus. Published by Elsevier B.V.
Free boundary problems and perpetual American strangles
(2013-08-01)
Chang, Ming-Chi
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
ON OPTIMAL STOPPING PROBLEMS FOR MATRIX-EXPONENTIAL JUMP-DIFFUSION PROCESSES
(2012-06-01)
Sheu, Yuan-Chung
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Tsai, Ming-Yao
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應用數學系
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Department of Applied Mathematics
In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.
ON THE DISCOUNTED PENALTY AT RUIN IN A JUMP-DIFFUSION MODEL
(2010-08-01)
Chen, Yu-Ting
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Sheu, Yuan-Chung
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應用數學系
;
Department of Applied Mathematics
In this paper, we study the discounted penalty in a perturbed compound Poisson model with two sided jumps. We prove second-order regularity of this function and investigate its asymptotic behavior at infinity Next, based on Boyarchenko and Levendorskii (2002), we justify an integro-differential equation for the discounted penalty.
Save Muscle Information-Unfiltered EEG Signal Helps Distinguish Sleep Stages
(2020-04-01)
Liu, Gi-Ren
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Lustenberger, Caroline
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Lo, Yu-Lun
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Liu, Wen-Te
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Sheu, Yuan-Chung
Based on the well-established biopotential theory, we hypothesize that the high frequency spectral information, like that higher than 100Hz, of the EEG signal recorded in the off-the-shelf EEG sensor contains muscle tone information. We show that an existing automatic sleep stage annotation algorithm can be improved by taking this information into account. This result suggests that if possible, we should sample the EEG signal with a high sampling rate, and preserve as much spectral information as possible.
The cutoff phenomenon for Ehrenfest chains
(2012-08-01)
Chen, Guan-Yu
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Fang, Yang-Jen
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
"We consider families of Ehrenfest chains and provide a simple criterion on the L-P-cutoff and the L-P-precutoff with specified initial states for 1 <= p < infinity. For the family with an L-P-cutoff, a cutoff time is described and a possible window is given. For the family without an L-P-precutoff, the exact order of the L-P-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity. (C) 2012 Elsevier B.V. All rights reserved."
THE L-2-CUTOFFS FOR REVERSIBLE MARKOV CHAINS
(2017-08-01)
Chen, Guan-Yu
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Hsu, Jui-Ming
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Sheu, Yuan-Chung
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應用數學系
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Department of Applied Mathematics
In this article, we considers reversible Markov chains of which L-2-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [J. Funct. Anal. 258 (2010) 2246-2315], while we provide here a completely different pathway to analyze the L-2-distance. Consequently, we obtain several considerably simplified criteria and this allows us to proceed advanced theoretical studies, including the comparison of cutoffs between discrete time lazy chains and continuous time chains. For an illustration, we consider product chains, a rather complicated model which could be involved to analyze using the method in [J. Funct. Anal. 258 (2010) 2246-2315], and derive the equivalence of their L-2- cutoffs.