scholarly journals ON THE INTERFACE BETWEEN OPTIMAL PERIODIC AND CONTINUOUS DIVIDEND STRATEGIES IN THE PRESENCE OF TRANSACTION COSTS

2016 ◽  
Vol 46 (3) ◽  
pp. 709-746 ◽  
Author(s):  
Benjamin Avanzi ◽  
Vincent Tu ◽  
Bernard Wong
Keyword(s):  
Lower Cost ◽  
Risk Model ◽  
Optimal Strategies ◽  
Hybrid Strategy ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
Barrier Type ◽  
Continuous Strategies ◽  
First Time

AbstractIn the classical optimal dividends problem, dividend decisions are allowed to be made at any point in time — according to acontinuousstrategy. Depending on the surplus process that is considered and whether dividend payouts are bounded or not, optimal strategies are generally of a band, barrier or threshold type. In reality, while surpluses change continuously, dividends are generally paid on a periodic basis. Because of this, the actuarial literature has recently considered strategies where dividends are only allowed to be distributed at (random) discrete times — according to aperiodicstrategy.In this paper, we focus on the Brownian risk model. In this context, theoptimalcontinuous and periodic strategies have previously been shown (independently of one another) to be of barrier type. For the first time, we consider a model where both strategies are used. In such ahybridstrategy, decisions are allowed to be made either at any time (continuously), or periodically at a lower cost. This proves optimal in some cases. We also determine under which combination of parameters a pure continuous, pure periodic or hybrid (including both continuous and periodic dividend payments) barrier strategy is optimal. Interestingly, the hybrid strategy lies in-between periodic and continuous strategies, which provides some interesting insights. Results are illustrated.

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 On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model

2007 ◽  
Vol 37 (02) ◽  
pp. 203-233 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Jürgen Hartinger ◽  
Stefan Thonhauser
Keyword(s):  
Risk Model ◽  
Infinite Horizon ◽  
Threshold Level ◽  
Threshold Strategy ◽  
Sparre Andersen Model ◽  
Dividend Payments ◽  
Andersen Model ◽  
Linear Barrier ◽  
Barrier Type ◽  
Premium Income

For the classical Cramér-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.

scholarly journals On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model

2007 ◽  
Vol 37 (2) ◽  
pp. 203-233 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Jürgen Hartinger ◽  
Stefan Thonhauser
Keyword(s):  
Risk Model ◽  
Infinite Horizon ◽  
Threshold Level ◽  
Threshold Strategy ◽  
Sparre Andersen Model ◽  
Dividend Payments ◽  
Andersen Model ◽  
Linear Barrier ◽  
Barrier Type ◽  
Premium Income

For the classical Cramér-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.

scholarly journals Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenguang Yu ◽  
Peng Guo ◽  
Qi Wang ◽  
Guofeng Guan ◽  
Yujuan Huang ◽  
...  
Keyword(s):  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Capital Injection ◽  
Surplus Process ◽  
Dividend Payments ◽  
Injection Line ◽  
Observation Times ◽  
Poisson Risk Model ◽  
Explicit Expressions

AbstractIn this paper, we model the insurance company’s surplus by a compound Poisson risk model, where the surplus process can only be observed at random observation times. It is assumed that the insurer observes its surplus level periodically to decide on dividend payments and capital injection at the interobservation time having an $\operatorname{Erlang}(n)$ Erlang ( n ) distribution. If the observed surplus level is greater than zero but less than injection line $b_{1} > 0$ b 1 > 0 , the shareholders should immediately inject a certain amount of capital to bring the surplus level back to the injection line $b_{1}$ b 1 . If the observed surplus level is larger than dividend line $b_{2}$ b 2 ($b_{2} > b_{1}$ b 2 > b 1 ), any excess of the surplus over $b_{2}$ b 2 is immediately paid out as dividends to the shareholders of the company. Ruin is declared when the observed surplus level is negative. We derive the explicit expressions of the Gerber–Shiu function, the expected discounted capital injection, and the expected discounted dividend payments. Numerical illustrations are also given to analyze the effect of random observation times on actuarial quantities.

scholarly journals Optimal dividends and capital injection under dividend restrictions

2020 ◽  
Vol 92 (3) ◽  
pp. 461-487 ◽  
Author(s):  
Kristoffer Lindensjö ◽  
Filip Lindskog
Keyword(s):  
Optimal Strategy ◽  
Stopping Time ◽  
Type I ◽  
Insurance Company ◽  
Type Ii ◽  
Dividend Payout ◽  
Optimal Dividends ◽  
Capital Injection ◽  
Surplus Process ◽  
Dividend Payments

AbstractWe study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout barrier in order for dividend payments to be allowed. Bankruptcy occurs if the surplus process becomes negative and there are proportional costs for capital injection. We show that one of the following strategies is optimal: (i) Pay dividends and inject capital in order to reflect the surplus process at an upper barrier and at 0, implying bankruptcy never occurs. (ii) Pay dividends in order to reflect the surplus process at an upper barrier and never inject capital—corresponding to absorption at 0—implying bankruptcy occurs the first time the surplus reaches zero. We show that if the costs of capital injection are low, then a sufficiently high dividend payout barrier will change the optimal strategy from type (i) (without bankruptcy) to type (ii) (with bankruptcy). Moreover, if the costs are high, then the optimal strategy is of type (ii) regardless of the dividend payout barrier. We also consider the possibility for the owner to choose a stopping time at which the insurance company is liquidated and the owner obtains a liquidation value. The uncontrolled surplus process is a Wiener process with drift.

scholarly journals A Lévy Risk Model with Ratcheting Dividend Strategy and Historic High-Related Stopping

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Aili Zhang ◽  
Zhang Liu
Keyword(s):  
Risk Model ◽  
Poisson Model ◽  
Risk Process ◽  
Closed Form Expression ◽  
Form Expression ◽  
Ruin Time ◽  
Scale Functions ◽  
Surplus Process ◽  
Dividend Payments ◽  
Special Cases

This paper focuses on the De Finetti’s dividend problem for the spectrally negative Lévy risk process, where the dividend is deducted from the surplus process according to the racheting dividend strategy which was firstly introduced in Albrecher et al. (2018). A major feature of the racheting strategy lies in which the dividend rate never decreases. Unlike the conventional studies, the closed form expression for the expected, accumulated, and discounted dividend payments until the draw-down time (rather than the ruin time) is obtained in terms of the scale functions corresponding to the underlying Lévy process. The optimal barrier for the ratcheting strategy is also studied, where the dividend rate can be increased. Finally, two special cases, where the scale functions are explicitly known, i.e., the Brownian motion with drift and the compound Poisson model, are considered to illustrate the main result.

scholarly journals A note on the optimal dividends paid in a foreign currency

2016 ◽  
Vol 11 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Julia Eisenberg ◽  
Paul Krühner
Keyword(s):  
Brownian Motion ◽  
Optimal Strategy ◽  
Value Function ◽  
Foreign Currency ◽  
Initial Capital ◽  
Brownian Motion With Drift ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
The Value Function

AbstractWe consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are declared or paid in a foreign currency. The currency fluctuation is modelled as a Lévy process. We consider both cases: restricted and unrestricted dividend payments. It turns out that the value function and the optimal strategy can be calculated explicitly.

scholarly journals Optimal Dividends Under a Ruin Probability Constraint

2006 ◽  
Vol 1 (2) ◽  
pp. 291-306 ◽  
Author(s):  
D. C. M. Dickson ◽  
S. Drekic
Keyword(s):  
Ruin Probability ◽  
Claim Amount ◽  
Present Value ◽  
Probabilistic Argument ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
Probability Constraint

ABSTRACTWe consider a classical surplus process modified by the payment of dividends when the insurer's surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.

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