On the joint distribution of surplus before and after ruin under a Markovian regime switching model

Ng, Andrew; Yang, Hailiang

doi:10.1016/j.spa.2005.09.008

Cited by 48 publications

(26 citation statements)

References 9 publications

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“…Ng and Yang (2006) give closed form solutions for the joint distribution of the surplus before and after ruin when the initial surplus is zero or when the claim amount distributions are phase-type distributed. Li and Lu (2007) study the moments of the present value of the dividend payments and the distribution of the total dividends prior to ruin for the Markov-modulated risk model modified by the introduction of a barrier dividend.…”

Section: !^Hmentioning

confidence: 99%

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The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model

Li¹,

Lu²

2008

ASTIN Bull.

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In this paper, we study the expected discounted penalty functions and their decompositions in a Markov-modulated risk process in which the rate for the Poisson claim arrivals and the distribution of the claim amounts vary in time depending on the state of an underlying (external) Markov jump process. The main feature of the model is the flexibility modeling the arrival process in the sense that periods with very frequent arrivals and periods with very few arrivals may alternate. Explicit formulas for the expected discounted penalty function at ruin, given the initial surplus, and the initial and terminal environment states, are obtained when the initial surplus is zero or when all the claim amount distributions are from the rational family. We also investigate the distributions of the maximum surplus before ruin and the maximum severity of ruin. The dividends-penalty identity is derived when the model is modified by applying a barrier dividend strategy. KEYWORDSMarkov-modulated risk model, expected discounted penalty function, maximum surplus before ruin, maximum severity of ruin, dividends-penalty identity.

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Section: !^Hmentioning

confidence: 99%

“…Using the same arguments as in Ng and Yang (2006), we obtain the following integro-differential equations for f i, j (u) by conditioning on the events occuring in a small interval [0, h]…”

Section: A System Of Integro-differential Equationsmentioning

confidence: 99%

The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model

Li¹,

Lu²

2008

ASTIN Bull.

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“…There are many papers published on ruin probabilities and the related problems under the Markov-modulated (or Markov regime-switching) risk model. Ng and Yang [3] give closed form solutions for the joint distribution of the surplus before and after ruin when the initial surplus is zero or when the claim amount distributions are phase-type distributed. Li and Lu [4] study the moments of the present value of the dividend payments and the distribution of the total dividends prior to ruin for the Markov-modulated risk model modified by the introduction of a barrier dividend.…”

Section: Introductionmentioning

confidence: 99%

Dividend Payments and Related Problems in a Markov-Dependent Insurance Risk Model under Absolute Ruin

Yu¹,

Huang²

2011

AJIBM

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“…Ng and Yang [4] obtain an upper bound for the joint distribution of surplus before and at ruin under the regime-switching model by using a martingale approach. Ng and Yang [5] present some explicit results for the joint distribution of surplus before and at ruin under this model in the cases of zero initial surplus and phase type claim size distributions, respectively. Li and Lu [6] investigate the moments of the dividend payments and related problems in a Markov-modulated risk model.…”

Section: Introductionmentioning

confidence: 99%

The Markovian Regime-Switching Risk Model with Constant Dividend Barrier under Absolute Ruin

Yu¹,

Huang²

2011

JMF

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In this paper, we consider the dividend payments prior to absolute ruin in a Markovian regime-switching risk process in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying Markov jump process. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the n th moment of the discounted dividend payments prior to absolute ruin and the expected discounted penalty function, given the initial environment state, are derived. Then, the matrix form of systems of integro-differential equations satisfied by the discounted penalty function are presented. Finally, we obtain the integro-differential equations satisfied by the time to reach the dividend barrier.

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On the joint distribution of surplus before and after ruin under a Markovian regime switching model

Cited by 48 publications

References 9 publications

The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model

The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model

Dividend Payments and Related Problems in a Markov-Dependent Insurance Risk Model under Absolute Ruin

The Markovian Regime-Switching Risk Model with Constant Dividend Barrier under Absolute Ruin

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