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1.
Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis
for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also
apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible
dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our
algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.
相似文献
2.
A local limit theorem for the probability of ruin 总被引:4,自引:0,他引:4
YIN ChuancunDepartment of Mathematics Qufu Normal University Qufu China 《中国科学A辑(英文版)》2004,47(5):711-721
In this paper, we give a result on the local asymptotic behaviour of the probability of ruin in a continuous-time risk model in which the inter-claim times have an Erlang distribution and the individual claim sizes have a distribution that belongs to S(v) with v≥ 0, but where the Lundberg exponent of the underlying risk process does not exist. 相似文献
3.
Shaochuan Lu 《Annals of the Institute of Statistical Mathematics》2012,64(1):87-106
In this paper, we introduce one type of Markov-Modulated Poisson Process (MMPP) whose arrival times are associated with state-dependent
marks. Statistical inference problems including the derivation of the likelihood, parameter estimation through EM algorithm
and statistical inference on the state process and the observed point process are addressed. A goodness-of-fit test is proposed
for MMPP with state-dependent marks by utilizing the theories of rescaling marked point process. We also perform some numerical
simulations to indicate the effects of different marks on the efficiencies and accuracies of MLE. The effects of the attached
marks on the estimation tend to be weakened for increasing data sizes. Then we apply these methods to characterize the occurrence
patterns of New Zealand deep earthquakes through a second-order MMPP with state-dependent marks. In this model, the occurrence
times and magnitudes of the deep earthquakes are associated with two levels of seismicity which evolves in terms of an unobservable
two-state Markov chain. 相似文献
4.
We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived. 相似文献
5.
We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.Supported in part by The Israel Science Foundation, grant no. 372/93-1. 相似文献
6.
On the analysis of the Gerber-Shiu discounted penalty function for risk processes with Markovian arrivals 总被引:1,自引:0,他引:1
Soohan Ahn 《Insurance: Mathematics and Economics》2007,41(2):234-249
In this paper, we consider an insurance risk model governed by a Markovian arrival claim process and by phase-type distributed claim amounts, which also allows for claim sizes to be correlated with the inter-claim times. A defective renewal equation of matrix form is derived for the Gerber-Shiu discounted penalty function and solved using matrix analytic methods. The use of the busy period distribution for the canonical fluid flow model is a key factor in our analysis, allowing us to obtain an explicit form of the Gerber-Shiu discounted penalty function avoiding thus the use of Lundberg’s fundamental equation roots. As a special case, we derive the triple Laplace transform of the time to ruin, surplus prior to ruin, and deficit at ruin in explicit form, further obtaining the discounted joint and marginal moments of the surplus prior to ruin and the deficit at ruin. 相似文献
7.
研究了跳服从Erlang(n)分布,随机观察时服从指数分布的对偶风险模型.假设在边值策略下红利分发只在观察时发生,建立了红利期望贴现函数V(u;b)的微积分方程组.给出了当收益额服从PH(m)分布时V(u;b)的解析解.探讨了当收益额服从指数分布时V(u;b)的具体求解方法. 相似文献
8.
In this paper, we study the Gerber-Shiu functions for a risk model with two independent classes of risks. We suppose that both of the two claim number processes are renewal processes with phase-type inter-claim times. By re-composing and analyzing the Markov chains associated with two given phase-type distributions, we obtain systems of integro-differential equations for two types of Gerber-Shiu functions. Explicit expressions for the Laplace transforms of the two types of Gerber-Shiu functions are established, respectively. And explicit results for the Gerber-Shiu functions are derived when the initial surplus is zero and when the two claim amount distributions are both from the rational family. Finally, an example is considered to illustrate the applicability of our main results. 相似文献
9.
Abstract We consider the pricing of options when the dynamics of the risky underlying asset are driven by a Markov-modulated jump-diffusion model. We suppose that the market interest rate, the drift and the volatility of the underlying risky asset switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The measure process is defined to be a generalized mixture of Poisson random measure and encompasses a general class of processes, for example, a generalized gamma process, which includes the weighted gamma process and the inverse Gaussian process. Another interesting feature of the measure process is that jump times and jump sizes can be correlated in general. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the underlying risky asset. We employ the generalized regime-switching Esscher transform to determine an equivalent martingale measure in the incomplete market setting. A system of coupled partial-differential-integral equations satisfied by the European option prices is derived. We also derive a decomposition result for an American put option into its European counterpart and early exercise premium. Simulation results of the model have been presented and discussed. 相似文献
10.
We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given. 相似文献
11.
In this paper, we consider the classical surplus process with a constant dividend barrier and a dependence structure between
the claim amounts and the inter-claim times. We derive an integro-differential equation with boundary conditions. Its solution
is expressed as the Gerber-Shiu discounted penalty function in the absence of a dividend barrier plus a linear combination
of a finite number of linearly independent particular solutions to the associated homogeneous integro-differential equation.
Finally, we obtain an explicit solution when the claim amounts are exponentially distributed and we investigate the effects
of dependence on ruin quantities. 相似文献
12.
本文考虑了索赔时间间距为phase-type分布时带干扰更新风险模型中的破产前最大盈余、破产后赤字的分布,建立了相应的积分-微分方程.最后,讨论了当索赔时间间距为Erlang(2)分布且索赔量满足指数分布时的特殊情形. 相似文献
13.
The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. 相似文献
14.
The Gerber-Shiu discounted penalty function in the risk process with phase-type interclaim times 总被引:1,自引:0,他引:1
In this paper, we consider the Gerber-Shiu discounted penalty function for the Sparre Anderson risk process in which the interclaim times have a phase-type distribution. By the Markov property of a joint process composed of the risk process and the underlying Markov process, we provide a new approach to prove the systems of integro-differential equations for the Gerber-Shiu functions. Closed form expressions for the Gerber-Shiu functions are obtained when the claim amount distribution is from the rational family. Finally we compute several numerical examples intended to illustrate the main results. 相似文献
15.
In this paper, we consider a Sparre Andersen model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the mth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber–Shiu functions. The special case where the inter-claim times are Erlang(2) distributed and the claim size distribution is exponential is considered in some details. 相似文献
16.
Li Jingchao Su Bihao Wei Zhenghong Nie Ciyu 《Methodology and Computing in Applied Probability》2022,24(3):2169-2194
In this paper, we consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results show that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency.
相似文献17.
This paper considers a perturbed renewal risk process in which the inter-claim times have a phase-type distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the mth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example. 相似文献
18.
19.
Zhao Yongxia 《应用概率统计》2013,29(5):495-514
In this paper, we study absolute ruin
problems for the Sparre Andersen risk process with generalized
Erlang()-distributed inter-claim times, investment and debit
interest. We first give a system of integro-differential equations
with certain boundary conditions satisfied by the expected
discounted penalty function at absolute ruin. Second, we obtain a
defective renewal equation under some special cases, then based on
the defective renewal equation we derive two asymptotic results for
the expected discounted penalty function when the initial surplus
tends to infinity for the light-tailed claims and heavy-tailed
claims, respectively. Finally, we investigate some explicit
solutions and numerical results for generalized Erlang(2)
inter-claim times and exponential claims. 相似文献