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 Optimising dividends and consumption under an exponential CIR as a discount factor

2020 ◽  
Vol 92 (2) ◽  
pp. 285-309
Author(s):  
Julia Eisenberg ◽  
Yuliya Mishura
Keyword(s):  
Brownian Motion ◽  
Optimal Strategy ◽  
Value Function ◽  
Insurance Company ◽  
Parameter Choice ◽  
Surplus Process ◽  
Dividend Payments ◽  
Cir Process ◽  
The Value Function ◽  
Special Parameter

AbstractWe consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spending/dividend payments under a discounting factor given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the value function. For the Brownian motion case, we are able to show that for a special parameter choice the optimal strategy is a constant-barrier strategy.

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 Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 276 ◽  
Author(s):  
Qingyou Yan ◽  
Le Yang ◽  
Tomas Baležentis ◽  
Dalia Streimikiene ◽  
Chao Qin
Keyword(s):  
Transaction Cost ◽  
Risk Information ◽  
Insurance Company ◽  
Optimal Control Strategy ◽  
Ruin Time ◽  
Discounted Cost ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend ◽  
A Company

This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process.

scholarly journals Dividend maximization in a hidden Markov switching model

2015 ◽  
Vol 32 (3-4) ◽  
pp. 143-158
Author(s):  
Michaela Szölgyenyi
Keyword(s):  
Markov Chain ◽  
Partial Information ◽  
Numerical Study ◽  
Insurance Company ◽  
Markov Switching Model ◽  
Switching Model ◽  
Surplus Process ◽  
Dividend Payments ◽  
Current State ◽  
Optimal Value

Abstract In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.

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 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 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 Optimal Expected Utility of Dividend Payments with Proportional Reinsurance under VaR Constraints and Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuzhen Wen ◽  
Chuancun Yin
Keyword(s):  
Optimal Strategy ◽  
Bellman Equation ◽  
Insurance Company ◽  
Time Value ◽  
Dividend Payments ◽  
Discounted Utility ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.

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.

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.

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