scholarly journals On Periodic Dividends for the Classical Risk Model with Debit Interest

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Risk Model ◽  
Classical Risk Model ◽  
Arrival Times ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Debit Interest ◽  
The Classical Risk Model

A periodic dividend problem is studied in this paper. We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored. First of all, three integro-differential equations for the expected discounted dividends are obtained. Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims. A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed. To demonstrate the existing results, we give some numerical examples.

scholarly journals ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

2014 ◽  
Vol 44 (3) ◽  
pp. 635-651 ◽  
Author(s):  
Chuancun Yin ◽  
Yuzhen Wen ◽  
Yongxia Zhao
Keyword(s):  
Lévy Process ◽  
Risk Model ◽  
Levy Process ◽  
Dual Model ◽  
Threshold Strategy ◽  
Classical Risk Model ◽  
Surplus Process ◽  
Optimal Dividend ◽  
Special Cases ◽  
The Classical Risk Model

AbstractIn this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

scholarly journals Recursive Calculation of Survival Probabilities

1991 ◽  
Vol 21 (2) ◽  
pp. 199-221 ◽  
Author(s):  
David C. M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Finite Time ◽  
Approximate Calculation ◽  
Risk Model ◽  
Classical Risk Model ◽  
Infinite Time ◽  
Numerical Examples ◽  
Survival Probabilities ◽  
Recursive Calculation ◽  
The Stability ◽  
The Classical Risk Model

AbstractIn this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

scholarly journals On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

2018 ◽  
Vol 55 (4) ◽  
pp. 1272-1286 ◽  
Author(s):  
Kei Noba ◽  
José-Luis Pérez ◽  
Kazutoshi Yamazaki ◽  
Kouji Yano
Keyword(s):  
Arrival Time ◽  
Arrival Times ◽  
Classical Sense ◽  
Capital Injection ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Injection Strategies

Abstract De Finetti’s optimal dividend problem has recently been extended to the case when dividend payments can be made only at Poisson arrival times. In this paper we consider the version with bail-outs where the surplus must be nonnegative uniformly in time. For a general spectrally negative Lévy model, we show the optimality of a Parisian-classical reflection strategy that pays the excess above a given barrier at each Poisson arrival time and also reflects from below at 0 in the classical sense.

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.

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 On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 511 ◽  
Author(s):  
Wenguang Yu ◽  
Peng Guo ◽  
Qi Wang ◽  
Guofeng Guan ◽  
Qing Yang ◽  
...  
Keyword(s):  
Risk Model ◽  
Observation Interval ◽  
Claim Amount ◽  
Insurance Company ◽  
Classical Risk Model ◽  
Numerical Examples ◽  
Compound Poisson Risk Model ◽  
Capital Injection ◽  
The Classical Risk Model ◽  
Injection Function

In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

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