Journal ArticleDOI
Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus
Yasutaka Shimizu,Zhimin Zhang +1 more
TLDR
In this paper, an estimator of the Gerber-shiu function via the empirical Fourier transform of the GSH was proposed, and the L 2 -consistency of the estimator under the assumption of high-frequency observation of the surplus process in a long term was evaluated.Abstract:
Consider an insurance surplus process driven by a Levy subordinator, which is observed at discrete time points. An estimator of the Gerber–Shiu function is proposed via the empirical Fourier transform of the Gerber–Shiu function. By evaluating its mean squared error, we show the L 2 -consistency of the estimator under the assumption of high-frequency observation of the surplus process in a long term. Simulation studies are also presented to show the finite sample performance of the proposed estimator.read more
Citations
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Journal ArticleDOI
Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion
TL;DR: In this paper, the authors used the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products, where the distribution of the time-to-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Levy process, explicit equations for the cosine coefficients are given.
Journal ArticleDOI
Estimating the Gerber–Shiu function in a Lévy risk model by Laguerre series expansion
Zhimin Zhang,Wen Su +1 more
TL;DR: A new method for estimating the Gerber–Shiu function in a pure jump Levy risk model is provided and the consistency property of this estimator when the sample size is large is derived.
Journal ArticleDOI
A new efficient method for estimating the Gerber–Shiu function in the classical risk model
Zhimin Zhang,Wen Su +1 more
TL;DR: In this article, a new efficient method for estimating the Gerber-Shiu discounted penalty function in the classical risk model is proposed, and the convergence rate of the estimate is derived.
Journal ArticleDOI
Computing the Gerber–Shiu function by frame duality projection
Wenyuan Wang,Zhimin Zhang +1 more
TL;DR: In this article, an efficient option pricing by frame duality with the fast Fourier transform was proposed. But this method is not suitable for option pricing in the context of financial transactions.
Journal ArticleDOI
Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion
Yang Yang,Wen Su,Zhimin Zhang +2 more
TL;DR: In this article, the authors study the statistical estimation of the discounted density of the deficit at ruin in the classical risk model, which is constructed by the two-dimensional Fourier cosine series expansion.
References
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Journal ArticleDOI
On the Time Value of Ruin
Hans U. Gerber,Elias S.W. Shiu +1 more
TL;DR: In this paper, the authors studied the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin, which can naturally be interpreted as discounting, and obtained explicit answers for zero initial surplus, very large initial surplus and arbitrary initial surplus if the claim amount distribution is exponential or a mixture of exponentials.
Journal ArticleDOI
Optimal capital structure and endogenous default
Bianca Hilberink,L. C. G. Rogers +1 more
TL;DR: This paper takes a model for the value of the firm's assets which allows for jumps, and finds that the spreads do not go to zero as maturity goes to zero.
Journal ArticleDOI
On the discounted penalty at ruin in a jump-diffusion and the perpetual put option
Hans U. Gerber,Bruno Landry +1 more
TL;DR: In this article, the authors considered the jump-diffusion that is obtained if an independent Wiener process is added to the surplus process of classical ruin theory, and examined the expected discounted value of a penalty at ruin; it satisfies a defective renewal equation which has a probabilistic interpretation.
Journal ArticleDOI
A generalized defective renewal equation for the surplus process perturbed by diffusion
TL;DR: In this article, the authors considered the surplus process of the classical continuous time risk model containing an independent diffusion process and proposed an asymptotic formula for the expected discounted penalty function.
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