scholarly journals On a Discrete-Time Risk Model with Random Income and a Constant Dividend Barrier

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Zhenhua Bao ◽  
Junqing Huang ◽  
Jing Wang
Keyword(s):  
Difference Equation ◽  
Discrete Time ◽  
Dividend Policy ◽  
Risk Model ◽  
Present Value ◽  
Numerical Example ◽  
Dividend Payments ◽  
Constant Dividend Barrier ◽  
The Difference

In this paper, a discrete-time risk model with random income and a constant dividend barrier is considered. Under such a dividend policy, once the insurer’s reserve hits the level b b > 0 , the excess of the reserve over b is paid off as dividends. We derive a homogeneous difference equation for the expected present value of dividend payments. Corresponding solution procedures for the difference equation are invested. Finally, we give a numerical example to illustrate the applicability of the results obtained.

scholarly journals Some Optimal Dividends Problems

2004 ◽  
Vol 34 (1) ◽  
pp. 49-74 ◽  
Author(s):  
David C.M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Present Value ◽  
Classical Risk Model ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
Constant Dividend Barrier ◽  
De Finetti ◽  
The Classical Risk Model

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

scholarly journals Some Optimal Dividends Problems

2004 ◽  
Vol 34 (01) ◽  
pp. 49-74 ◽  
Author(s):  
David C.M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Present Value ◽  
Classical Risk Model ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
Constant Dividend Barrier ◽  
De Finetti ◽  
The Classical Risk Model

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

scholarly journals Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

2007 ◽  
Vol 44 (2) ◽  
pp. 420-427 ◽  
Author(s):  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Risk Model ◽  
Levy Processes ◽  
Short Paper ◽  
Insurance Risk ◽  
Present Value ◽  
Dividend Payments ◽  
Insurance Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

scholarly journals The probability of ruin in a reinsurance risk model with m-dependence assumptions

2021 ◽  
Author(s):  
HOANG NGUYEN HUY ◽  
NGUYEN CHUNG
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Random Variables ◽  
Upper Bounds ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Numerical Example ◽  
Surplus Process ◽  
Inductive Methods

In this article, we investigate a discrete-time risk model. The risk model includes the quota- (α,β) reinsurance contract effect on the surplus process. The premium process and claim process are assumed to be m-dependent sequences of i.i.d. non-negative random variables. Using Martingale and inductive methods, we obtain upper bounds for ultimate ruin probability of an insurance company. Finally, we present a numerical example to show the efficiency of the methods.

The density of the time of ruin in the classical risk model with a constant dividend barrier

2013 ◽  
Vol 8 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Shuanming Li ◽  
Yi Lu
Keyword(s):  
Density Function ◽  
Risk Model ◽  
Special Functions ◽  
Laplace Transforms ◽  
Classical Risk Model ◽  
Dividend Payments ◽  
Time Of Ruin ◽  
Constant Dividend Barrier ◽  
The Time Of Ruin ◽  
The Classical Risk Model

AbstractIn this paper, we investigate the density function of the time of ruin in the classical risk model with a constant dividend barrier. When claims are exponentially distributed, we derive explicit expressions for the density function of the time of ruin and its decompositions: the density of the time of ruin without dividend payments and the density of the time of ruin with dividend payments. These densities are obtained based on their Laplace transforms, and expressed in terms of some special functions which are computationally tractable. The Laplace transforms are being inverted using a magnificent tool, the Lagrange inverse formula, developed in Dickson and Willmot (2005). Several numerical examples are given to illustrate our results.

scholarly journals The implied cost of capital of government’s claim and the present value of tax shields: A numerical example

2014 ◽  
Vol 3 (1) ◽  
pp. 40
Author(s):  
M. B.J. Schauten ◽  
B. Tans
Keyword(s):  
Discount Rate ◽  
Cost Of Capital ◽  
Present Value ◽  
Numerical Example ◽  
Implied Cost Of Capital ◽  
Tax Shields ◽  
The Difference ◽  
The Cost

This paper provides a numerical example of how to calculate the cost of capital of government’s claim (rg) and the present value of tax shields. Schauten and Tans (2006) show for the models used in Myers (1974), Miles and Ezzell (1980) and Harris and Pringle (1985), that the present value of tax shields is equal to the difference between the present value of the expected taxes paid by the unlevered firm and the levered firm, with each of the models’ implied rg as discount rate. We discuss a numerical example using the valuation framework by Schauten and Tans (2006) and give a logic explanation for the low implied rgs of Miles and Ezzell’s and Harris and Pringle’s model.

Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

2007 ◽  
Vol 44 (02) ◽  
pp. 420-427 ◽  
Author(s):  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Risk Model ◽  
Levy Processes ◽  
Short Paper ◽  
Insurance Risk ◽  
Present Value ◽  
Dividend Payments ◽  
Insurance Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

scholarly journals Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

2007 ◽  
Vol 44 (02) ◽  
pp. 420-427 ◽  
Author(s):  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Risk Model ◽  
Levy Processes ◽  
Short Paper ◽  
Insurance Risk ◽  
Present Value ◽  
Dividend Payments ◽  
Insurance Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

scholarly journals Optimal Dividend Policy In Discrete Time

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Ewa Marciniak ◽  
Jakub Trybuła
Keyword(s):  
Discrete Time ◽  
Dividend Policy ◽  
Value Function ◽  
Bank Loan ◽  
Numerical Example ◽  
A Value ◽  
Optimal Dividend ◽  
Optimal Dividend Policy

AbstractA problem of optimal dividend policy for a firm with a bank loan is considered. A regularity of a value function is established. A numerical example of calculating value function is given

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