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Threshold Estimation for a Spectrally Negative Lévy Process
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Consider a spectrally negative Lévy process with unknown diffusion coefficient and Lévy measure and suppose that the high frequency trading data is given. We use the techniques of threshold estimation and regularized Laplace inversion to obtain the estimator of survival probability for a spectrally negative Lévy process.
Honglong You, Chuncun Yin, Wenguang Yu
wiley +1 more source
An Uncertain Alternating Renewal Insurance Risk Model
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 The claim process in an insurance risk model with uncertainty is traditionally described by an uncertain renewal reward process. However, the claim process actually includes two processes, which are called the report process and the payment process, respectively.
Jia Zhai +4 more
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The Gerber–Shiu discounted penalty function in the stationary renewal risk model [PDF]
Insurance: Mathematics and Economics, 2003 The aim of this article is to investigate various properties associated with the stationary renewal risk process. In the introductory Section 1, the authors review the ordinary renewal risk model, the stationary (equilibrium) renewal risk process, the invariance property between the stationary renewal risk and the classical models, the discounted ...
Willmot, Gordon E., Dickson, David C. M.
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An Optimal Portfolio Problem of DC Pension with Input‐Delay and Jump‐Diffusion Process
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 In this paper, an optimal portfolio control problem of DC pension is studied where the time interval between the implementation of investment behavior and its effectiveness (hereafter input‐delay) is particularly focused. There are two assets available for investment: a risk‐free cash bond and a risky stock with a jump‐diffusion process. And the wealth
Weixiang Xu, Jinggui Gao, Wenguang Yu
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Pricing of Margin Call Stock Loan Based on the FMLS
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 In common stock loan, lenders face the risk that their loans will not be repaid if the stock price falls below loan, which limits the issuance and circulation of stock loans. The empirical test suggests that the log‐return series of stock price in the US market reject the normal distribution and admit instead a subclass of the asymmetric distribution ...
Kaili Xiang +3 more
wiley +1 more source
PHASE-TYPE APPROXIMATION OF THE GERBER-SHIU FUNCTION
Journal of the Operations Research Society of Japan, 2017 16 pages. Forthcoming in the Journal of the Operations Research Society of Japan, vol. 60, no. 3, 2017 (special issue of the 60th anniversary of the Operations Research Society of Japan)
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Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes [PDF]
, 2016 Inspired by works of Landriault et al. [11, 12], we study the Gerber{Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Levy insurance risk process.
Pardo, Juan Carlos +3 more
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Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process [PDF]
, 2023 We consider a two-dimensional risk model with simultaneous Poisson arrivals of claims. Each claim of the first input process is at least as large as the corresponding claim of the second input process.
Mandjes, M. +8 more
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International Journal of Mathematics for Industry, 2023 This paper studies the Gerber–Shiu function for the insurance surplus process with additional investment under the Bachelier model. The Gerber–Shiu function allows us to study the moments of the time of ruin, which is the first time that the surplus is negative.
Sutipon Punaluek, Yuri Imamura
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