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 (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 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 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 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.

Some Optimal Dividend Problems for a Surplus Process with Stochastic Interest

2010 ◽  
Vol 108-111 ◽  
pp. 1097-1102
Author(s):  
Wen Guang Yu
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Closed Form ◽  
Present Value ◽  
Integro Differential Equation ◽  
Surplus Process ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Stochastic Interest

In this paper, some results on the dividend payments prior to ruin in the classical surplus process with stochastic interest are derived. An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved. Furthermore, closed-form expressions for exponential claims are given.

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 Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

2019 ◽  
Vol 24 (1) ◽  
pp. 21 ◽  
Author(s):  
Christian Kasumo
Keyword(s):  
Integral Equation ◽  
Ruin Probability ◽  
Stock Price ◽  
Risk Model ◽  
Vital Role ◽  
Insurance Companies ◽  
Claim Amount ◽  
Proportional Reinsurance ◽  
Investment Return ◽  
Return Process

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard a Black–Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton–Jacobi–Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed individual claim amount distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

scholarly journals On the time value of absolute ruin with debit interest

2007 ◽  
Vol 39 (02) ◽  
pp. 343-359 ◽  
Author(s):  
Jun Cai
Keyword(s):  
Differential Equations ◽  
Ruin Probability ◽  
Expected Discounted Penalty Function ◽  
Surplus Process ◽  
Absolute Ruin ◽  
The Laplace Transform ◽  
The Absolute ◽  
Heavy Tailed ◽  
Premium Income ◽  
Debit Interest

Assume that the surplus of an insurer follows a compound Poisson surplus process. When the surplus is below zero or the insurer is on deficit, the insurer could borrow money at a debit interest rate to pay claims. Meanwhile, the insurer will repay the debts from her premium income. The negative surplus may return to a positive level. However, when the negative surplus is below a certain critical level, the surplus is no longer able to be positive. Absolute ruin occurs at this moment. In this paper, we study absolute ruin questions by defining an expected discounted penalty function at absolute ruin. The function includes the absolute ruin probability, the Laplace transform of the time to absolute ruin, the deficit at absolute ruin, the surplus just before absolute ruin, and many other quantities related to absolute ruin. First, we derive a system of integro-differential equations satisfied by the function and obtain a defective renewal equation that links the integro-differential equations in the system. Second, we show that when the initial surplus goes to infinity, the absolute ruin probability and the classical ruin probability are asymptotically equal for heavy-tailed claims while the ratio of the absolute ruin probability to the classical ruin probability goes to a positive constant that is less than one for light-tailed claims. Finally, we give explicit expressions for the function for exponential claims.

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