scholarly journals Gerber-Shiu Function in a Discrete-time Risk Model with Dividend Strategy

2021 ◽  
pp. 97-110
Author(s):  
Junqing Huang ◽  
Zhenhua Bao
Keyword(s):  
General Theory ◽  
Discrete Time ◽  
Difference Equations ◽  
Penalty Function ◽  
Risk Model ◽  
Fundamental Equation ◽  
Numerical Examples ◽  
Premium Rate ◽  
Discounted Penalty Function ◽  
Constant Dividend Barrier

In this paper, a discrete-time risk model with dividend strategy and a general premium rate is considered. Under such a strategy, once the insurer’s surplus hits a constant dividend barrier , dividends are paid off to shareholders at  instantly. Using the roots of a generalization of Lundberg’s fundamental equation and the general theory on difference equations, two difference equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results obtained are utilized to derive the probability of ultimate ruin when the claim sizes is a mixture of two geometric distributions. Numerical examples are also given to illustrate the applicability of the results obtained.

scholarly journals Ruin Probabilities of a Discrete-time Multi-risk Model

2015 ◽  
Vol 44 (4) ◽  
pp. 367-379 ◽  
Author(s):  
Andrius Grigutis ◽  
Agneška Korvel ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Arrival Time ◽  
Risk Model ◽  
Recursive Formula ◽  
Ruin Probabilities ◽  
Numerical Examples ◽  
Premium Rate ◽  
Insurance Business ◽  
Independent Series

In this work,  we investigate a  multi-risk model describing insurance business with  two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed   inter-arrival time. Claim amounts occur until they   can be compensated by a common premium rate and the initial insurer's surplus.  In this article, wederive a recursive formula for calculation of finite-time ruin probabilities. In the case of bi-risk model, we present a procedure to calculate the ultimate ruin probability. We add several numerical examples illustrating application  of the derived formulas.DOI: http://dx.doi.org/10.5755/j01.itc.44.4.8635

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 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.

The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Informatica ◽  
2018 ◽  
Vol 29 (4) ◽  
pp. 733-756 ◽  
Author(s):  
Olga Navickienė ◽  
Jonas Sprindys ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Penalty Function ◽  
Risk Model ◽  
Discounted Penalty Function

scholarly journals On a Discrete Markov-Modulated Risk Model with Random Premium Income and Delayed Claims

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Changwei Nie ◽  
Mi Chen ◽  
Haiyan Liu ◽  
Wenguang Yu
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Difference Equations ◽  
Risk Model ◽  
Numerical Examples ◽  
Finite State ◽  
Constant Dividend Barrier ◽  
Markov Modulated ◽  
Premium Income ◽  
Finite State Space

In this paper, a discrete Markov-modulated risk model with delayed claims, random premium income, and a constant dividend barrier is proposed. It is assumed that the random premium income and individual claims are affected by a Markov chain with finite state space. The model proposed is an extension of the discrete semi-Markov risk model with random premium income and delayed claims. Explicit expressions for the total expected discounted dividends until ruin are obtained by the method of generating function and the theory of difference equations. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples.

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