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Zbigniew Palmowski - One of the best experts on this subject based on the ideXlab platform.
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two dimensional Ruin Probability for subexponential claim size
Probability and Mathematical Statistics, 2018Co-Authors: Zbigniew Palmowski, Sergey Foss, Dmitry Korshunov, Tomasz RolskiAbstract:TWO-DIMENSIONAL Ruin Probability FOR SUBEXPONENTIAL CLAIM SIZEWe analyse the asymptotics of Ruin probabilities of two insurance companies or two branches of the same company that divide between them both claims and premiums in some specified proportions when the initial reserves of both companies tend to infinity, and generic claim size is subexponential.
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binomial discrete time Ruin Probability with parisian delay
arXiv: Probability, 2014Co-Authors: Irmina Czarna, Zbigniew Palmowski, Przemys Law światekAbstract:In this paper we analyze discrete time Parisian Ruin Probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We identify expressions for the Ruin probabilities with finite and infinite-time horizon. We find also their asymptotics when reserves tends to infinity. Finally, we calculate these probabilities for a few explicit examples. {\bf Keywords:} discrete time risk process, Ruin Probability, asymptotics, Parisian Ruin.
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parisian Ruin Probability for spectrally negative levy processes
Bernoulli, 2013Co-Authors: Ronnie Loeffen, Irmina Czarna, Zbigniew PalmowskiAbstract:In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian Ruin Probability, which is defined by the Probability that the process exhibits an excursion below zero which length exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process
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parisian Ruin Probability for spectrally negative l e vy processes
Research Papers in Economics, 2013Co-Authors: Ronnie Loeffen, Irmina Czarna, Zbigniew PalmowskiAbstract:In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian Ruin Probability, which is defined by the Probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process and the distribution of the process at time r.
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Ruin Probability with parisian delay for a spectrally negative levy risk process
Journal of Applied Probability, 2011Co-Authors: Irmina Czarna, Zbigniew PalmowskiAbstract:In this paper we analyze the so-called Parisian Ruin Probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0. We focus on a general spectrally negative Levy insurance risk process. For this class of processes, we derive an expression for the Ruin Probability in terms of quantities that can be calculated explicitly in many models. We find its Cramer-type and convolution-equivalent asymptotics when reserves tend to ∞. Finally, we analyze some explicit examples.
Yasutaka Shimizu - One of the best experts on this subject based on the ideXlab platform.
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parametric inference for Ruin Probability in the classical risk model
Statistics & Probability Letters, 2018Co-Authors: Takayoshi Oshime, Yasutaka ShimizuAbstract:Abstract Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the Ruin Probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the Ruin Probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of Ruin Probability.
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edgeworth type expansion of Ruin Probability under levy risk processes in the small loading asymptotics
Scandinavian Actuarial Journal, 2014Co-Authors: Yasutaka ShimizuAbstract:This paper presents an asymptotic expansion of the ultimate Ruin Probability under Levy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the Ruin Probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to Ruin, and the scale function of spectrally negative Levy processes.
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edgeworth type expansion of Ruin Probability under levy risk processes in the small loading asymptotics
Social Science Research Network, 2012Co-Authors: Yasutaka ShimizuAbstract:This paper presents an asymptotic expansion of the ultimate Ruin Probability under Levy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for the compound geometric sum. We give higher-order expansion of the Ruin Probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to Ruin, and the scale function of spectrally negative Levy processes.
Qihe Tang - One of the best experts on this subject based on the ideXlab platform.
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a hybrid estimate for the finite time Ruin Probability in a bivariate autoregressive risk model with application to portfolio optimization
The North American Actuarial Journal, 2012Co-Authors: Qihe Tang, Zhongyi YuanAbstract:Abstract Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another auto regressive process, independent of the former one. We derive an asymptotic formula for the finite-time Ruin Probability and propose a hybrid method, combining simulation with asymptotics, to compute this Ruin Probability more efficiently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the Ruin Probability.
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THE FINITE-TIME Ruin Probability OF THE COMPOUND POISSON MODEL WITH CONSTANT INTEREST FORCE
Journal of Applied Probability, 2005Co-Authors: Qihe TangAbstract:In this paper, we establish a simple asymptotic formula for the finite-time Ruin Probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate Ruin Probability and, in particular, is uniform for all time horizons when the claim size distribution is regularly varying tailed.
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the Ruin Probability of a discrete time risk model under constant interest rate with heavy tails
Scandinavian Actuarial Journal, 2004Co-Authors: Qihe TangAbstract:This paper investigates the ultimate Ruin Probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the Ruin Probability is derived and compared to existing results.
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precise estimates for the Ruin Probability in finite horizon in a discrete time model with heavy tailed insurance and financial risks
Stochastic Processes and their Applications, 2003Co-Authors: Qihe Tang, G. Sh. TsitsiashviliAbstract:This paper investigates the Probability of Ruin within finite horizon for a discrete time risk model, in which the reserve of an insurance business is currently invested in a risky asset. Under assumption that the risks are heavy tailed, some precise estimates for the finite time Ruin Probability are derived, which confirm a folklore that the Ruin Probability is mainly determined by whichever of insurance risk and financial risk is heavier than the other. In addition, some discussions on the heavy tails of the sum and product of independent random variables are involved, most of which have their own merits.
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estimates for the Ruin Probability in the classical risk model with constant interest force in the presence of heavy tails
Insurance Mathematics & Economics, 2002Co-Authors: Dimitrios G Konstantinides, Qihe Tang, G. Sh. TsitsiashviliAbstract:In this paper we investigate the Ruin Probability in the classical risk model under a positive constant interest force. We restrict ourselves to the case where the claim size is heavy-tailed, i.e. the equilibrium distribution function (e.d.f.) of the claim size belongs to a wide subclass of the subexponential distributions. Two-sided estimates for the Ruin Probability are developed by reduction from the classical model without interest force. © 2002 Elsevier Science B.V. All rights reserved.
Hailiang Yang - One of the best experts on this subject based on the ideXlab platform.
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asymptotic results for Ruin Probability in a two dimensional risk model with stochastic investment returns
Journal of Computational and Applied Mathematics, 2017Co-Authors: Fenglong Guo, Dingcheng Wang, Hailiang YangAbstract:Abstract This paper considers a two-dimensional time-dependent risk model with stochastic investment returns. In the model, an insurer operates two lines of insurance businesses sharing a common claim number process and can invest its surplus into some risky assets. The claim number process is assumed to be a renewal counting process and the investment return is modeled by a geometric Levy process. Furthermore, claim sizes of the two insurance businesses and their common inter-arrival times correspondingly follow a three-dimensional Sarmanov distribution. When claim sizes of the two lines of insurance businesses are heavy tailed, we establish some uniform asymptotic formulas for the Ruin Probability of the model over certain time horizon. Also, we show the accuracy of these asymptotic estimates for the Ruin Probability under the risk model by numerical studies.
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nonparametric estimation for the Ruin Probability in a levy risk model under low frequency observation
Insurance Mathematics & Economics, 2014Co-Authors: Zhimin Zhang, Hailiang YangAbstract:In this paper, we propose a nonparametric estimator for the Ruin Probability in a spectrally negative Levy risk model based on low-frequency observation. The estimator is constructed via the Fourier transform of the Ruin Probability. The convergence rates of the estimator are studied for large sample size. Some simulation results are also given to show the performance of the proposed method when the sample size is finite.
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on a nonparametric estimator for Ruin Probability in the classical risk model
Scandinavian Actuarial Journal, 2014Co-Authors: Zhimin Zhang, Hailiang Yang, Hu YangAbstract:In this paper, we present a nonparametric estimator for Ruin Probability in the classical risk model with unknown claim size distribution. We construct the estimator by Fourier inversion and kernel density estimation method. Under some conditions imposed on the kernel, bandwidth and claim size density, we present some large sample properties of the estimator. Some simulation studies are also given to show the finite sample performance of the estimator.
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nonparametric estimate of the Ruin Probability in a pure jump levy risk model
Insurance Mathematics & Economics, 2013Co-Authors: Zhimin Zhang, Hailiang YangAbstract:In this paper, we propose a nonparametric estimator of Ruin Probability in a Levy risk model. The aggregate claims process X={Xt,≥0} is modeled by a pure-jump Levy process. Assume that high-frequency observed data on X are available. The estimator is constructed based on the Pollaczek–Khinchin formula and Fourier transform. Risk bounds as well as a data-driven cut-off selection methodology are presented. Simulation studies are also given to show the finite sample performance of our estimator.
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estimates for the absolute Ruin Probability in the compound poisson risk model with credit and debit interest
Journal of Applied Probability, 2008Co-Authors: Hailiang YangAbstract:In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute Ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute Ruin Probability of this model. First we investigate the asymptotic behavior of the absolute Ruin Probability when the claim size distribution is light tailed. Then we study the case where the common distribution of claim sizes are heavy tailed.
Irmina Czarna - One of the best experts on this subject based on the ideXlab platform.
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parisian Ruin Probability with a lower ultimate bankrupt barrier
Scandinavian Actuarial Journal, 2016Co-Authors: Irmina CzarnaAbstract:The paper deals with a Ruin problem, where there is a Parisian delay and a lower ultimate bankrupt barrier. In this problem, we will say that a risk process get Ruined when it stays below zero longer than a fixed amount of time ζ > 0 or goes below a fixed level −a. We focus on a general spectrally negative Levy insurance risk process. For this class of processes, we identify the Laplace transform of the Ruin Probability in terms of so-called q-scale functions. We find its Cramer-type and convolution-equivalent asymptotics when reserves tends to infinity. Finally, we analyze few explicit examples.
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binomial discrete time Ruin Probability with parisian delay
arXiv: Probability, 2014Co-Authors: Irmina Czarna, Zbigniew Palmowski, Przemys Law światekAbstract:In this paper we analyze discrete time Parisian Ruin Probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We identify expressions for the Ruin probabilities with finite and infinite-time horizon. We find also their asymptotics when reserves tends to infinity. Finally, we calculate these probabilities for a few explicit examples. {\bf Keywords:} discrete time risk process, Ruin Probability, asymptotics, Parisian Ruin.
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parisian Ruin Probability for spectrally negative levy processes
Bernoulli, 2013Co-Authors: Ronnie Loeffen, Irmina Czarna, Zbigniew PalmowskiAbstract:In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian Ruin Probability, which is defined by the Probability that the process exhibits an excursion below zero which length exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process
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parisian Ruin Probability for spectrally negative l e vy processes
Research Papers in Economics, 2013Co-Authors: Ronnie Loeffen, Irmina Czarna, Zbigniew PalmowskiAbstract:In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian Ruin Probability, which is defined by the Probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process and the distribution of the process at time r.
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Ruin Probability with parisian delay for a spectrally negative levy risk process
Journal of Applied Probability, 2011Co-Authors: Irmina Czarna, Zbigniew PalmowskiAbstract:In this paper we analyze the so-called Parisian Ruin Probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0. We focus on a general spectrally negative Levy insurance risk process. For this class of processes, we derive an expression for the Ruin Probability in terms of quantities that can be calculated explicitly in many models. We find its Cramer-type and convolution-equivalent asymptotics when reserves tend to ∞. Finally, we analyze some explicit examples.
