Duration of negative surplus for a two state Markov-modulated risk model

2010 ◽  
Vol 30 (4) ◽  
pp. 1167-1173
Author(s):  
Ma Xuemin ◽  
Yuan Haili ◽  
Hu Yijun
Keyword(s):  
Risk Model ◽  
Markov Modulated

scholarly journals Ruin problems in Markov-modulated risk models

2017 ◽  
Vol 12 (1) ◽  
pp. 23-48 ◽  
Author(s):  
David C.M. Dickson ◽  
Marjan Qazvini
Keyword(s):  
Continuous Time ◽  
Risk Model ◽  
Numerical Algorithms ◽  
Binomial Model ◽  
Risk Models ◽  
Time Of Ruin ◽  
Compound Binomial ◽  
Compound Binomial Model ◽  
Markov Modulated ◽  
The Time Of Ruin

AbstractChen et al. (2014), studied a discrete semi-Markov risk model that covers existing risk models such as the compound binomial model and the compound Markov binomial model. We consider their model and build numerical algorithms that provide approximations to the probability of ultimate ruin and the probability and severity of ruin in a continuous time two-state Markov-modulated risk model. We then study the finite time ruin probability for a discrete m-state model and show how we can approximate the density of the time of ruin in a continuous time Markov-modulated model with more than two states.

Constant barrier strategies in a two-state Markov-modulated dual risk model

2011 ◽  
Vol 27 (4) ◽  
pp. 679-690 ◽  
Author(s):  
Xue-min Ma ◽  
Kui Luo ◽  
Guang-ming Wang ◽  
Yi-jun Hu
Keyword(s):  
Risk Model ◽  
Dual Risk Model ◽  
Markov Modulated

scholarly journals Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Chebyshev Polynomial ◽  
Polynomial Approximation ◽  
Risk Model ◽  
Arbitrary Distribution ◽  
System Of Differential Equations ◽  
Numerical Result ◽  
Chebyshev Polynomial Approximation ◽  
Markov Modulated

This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.

scholarly journals Perturbed MAP Risk Models with Dividend Barrier Strategies

2009 ◽  
Vol 46 (2) ◽  
pp. 521-541 ◽  
Author(s):  
Eric C. K. Cheung ◽  
David Landriault
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Arrival Process ◽  
Risk Models ◽  
Expected Discounted Penalty Function ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Discounted Penalty Function ◽  
Markov Modulated ◽  
Expected Discounted Penalty

In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

scholarly journals Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

2005 ◽  
Vol 35 (02) ◽  
pp. 351-361 ◽  
Author(s):  
Andrew C.Y. Ng ◽  
Hailiang Yang
Keyword(s):  
Regime Switching ◽  
Joint Distribution ◽  
Risk Model ◽  
Insurance Risk ◽  
Additive Process ◽  
Deficit At Ruin ◽  
Markov Additive Process ◽  
The Deficit At Ruin ◽  
Markov Modulated ◽  
Markovian Regime Switching

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.

scholarly journals Perturbed MAP Risk Models with Dividend Barrier Strategies

2009 ◽  
Vol 46 (02) ◽  
pp. 521-541 ◽  
Author(s):  
Eric C. K. Cheung ◽  
David Landriault
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Arrival Process ◽  
Risk Models ◽  
Expected Discounted Penalty Function ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Discounted Penalty Function ◽  
Markov Modulated ◽  
Expected Discounted Penalty

In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

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