Results 21 to 30 of about 5,349,529 (108)
The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model [PDF]
ASTIN Bulletin, 2004 We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under ...
Avram, Florin, Usábel, Miguel
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Estimating the Gerber‐Shiu Function in a Compound Poisson Risk Model with Stochastic Premium Income
Discrete Dynamics in Nature and Society, Volume 2019, Issue 1, 2019., 2019 In this paper, we consider the compound Poisson risk model with stochastic premium income. We propose a new estimation of Gerber‐Shiu function by an efficient method: Fourier‐cosine series expansion. We show that the estimator is easily computed and has a fast convergence rate.
Yunyun Wang +3 more
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A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
Abstract and Applied Analysis, Volume 2016, Issue 1, 2016., 2016 This paper investigates the two‐sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two‐sided barriers and the value at the first passage ...
Djilali Ait-Aoudia, Lucas Jodar
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INVESTIGATION OF THE GERBER-SHIU DISCOUNTED PENALTY FUNCTION ON FINITE TIME HORIZON
Information Technology and Control, 2010 In this paper, the classical risk model with exponential claim sizes is considered. The explicit expression of the Gerber-Shiu discounted penalty function (x; ; t) and discounted moments m(x; ; t) on finite time horizon is obtained, where > 0 is the force of interest, x - the initial reserve.
Jelena Kočetova, Jonas Šiaulys
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Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 This paper studies the first passage times to constant boundaries for mixed‐exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained.
Chuancun Yin +4 more
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Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process
Huiming Zhu +4 more
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The Gerber-Shiu discounted penalty function in the stationary renewal risk model [PDF]
, 2002 ISBN 0734028911 research paper no. 102The discounted penalty function introduced by Gerber and Shiu (1998) is considered in the stationary renewal risk model, where it is expressed in terms of the same discounted penalty function in the ordinary renewal ...
Dickson, David C. M., Willmot, Gordon E.
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On the discounted penalty function in the discrete time stationary renewal risk model [PDF]
, 2010 In this paper we consider the discrete time stationary renewal risk model. We express the Gerber–Shiu discounted penalty function in the stationary renewal risk model in terms of the corresponding Gerber–Shiu function in the ordinary model. In particular,
Wang, Jing, Bao, Zhen-hua
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The Ornstein‐Uhlenbeck‐Type Model with a Hybrid Dividend Strategy
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 We consider the Ornstein‐Uhlenbeck‐type model. We first introduce the model and then find the ordinary differential equations and boundary conditions satisfied by the dividend functions; closed‐form solutions for the dividend value functions are given. We also study the distribution of the time value of ruin.
Dan Zhu, Chuancun Yin, Mina Abd-El-Malek
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Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income
Mathematical Problems in Engineering, Volume 2013, Issue 1, 2013., 2013 The compound binomial insurance risk model is extended to the case where the premium income process, based on a binomial process, is no longer a constant premium rate of 1 per period and insurer pays a dividend of 1 with a probability q0 when the surplus is greater than or equal to a nonnegative integer b. The recursion formulas for expected discounted
Wenguang Yu, Guangchen Wang
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