Classical and singular stochastic control for the optimal dividend policy when there is regime switching

Sotomayor, Luz R.; Cadenillas, Abel

doi:10.1016/j.insmatheco.2011.01.002

Cited by 54 publications

(36 citation statements)

References 32 publications

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“…In particular, we assume here that we can observe the process (ε t ), whereas in practice one will not be able to determine the current state of the process (this is somewhat akin to the approach of Albrecher & Hartinger [2] in a different context). Recently, Sotomayor & Cadenillas [18] considered a Markov switching environment for a diffusion process with state-dependent coefficients.…”

Section: State-dependent Barrier Strategiesmentioning

confidence: 99%

On optimal dividend strategies in insurance with a random time horizon

Albrecher¹,

Thonhauser²

2012

Advances in Statistics, Probability and Actuarial Science

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For the classical compound Poisson surplus process of an insurance portfolio we investigate the problem of how to optimally pay out dividends to shareholders if the criterion is to maximize the expected discounted dividend payments until the time of ruin or a random time horizon, whichever is smaller. We explicitly solve this problem for an exponential time horizon and exponential claim sizes. Furthermore, we study the case of an Erlang(2) time horizon by introducing an external state process and derive the solution under the assumption that the external state process is observable. The results are illustrated by numerical examples.

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Section: State-dependent Barrier Strategiesmentioning

confidence: 99%

On optimal dividend strategies in insurance with a random time horizon

Albrecher¹,

Thonhauser²

2012

Advances in Statistics, Probability and Actuarial Science

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“…Such an application was developed by Zhu and Chen [25]. Different dividend optimization problems, but still in a regime-switching setting, have been recently treated by Sotomayor and Cadenillas [20], Wei et al [21], [22], [23], and Zhu [24].…”

Section: Introductionmentioning

confidence: 99%

Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching

Jiang¹

2015

J. Appl. Probab.

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In this paper we study the optimal dividend payments for a company of limited liability whose cash reserves in the absence of dividends follow a Markov-modulated jumpdiffusion process with positive drifts and negative exponential jumps, where parameters and discount rates are modulated by a finite-state irreducible Markov chain. The main aim is to maximize the expected cumulative discounted dividend payments until bankruptcy time when cash reserves are nonpositive for the first time. We extend the results of Jiang and Pistorius [15] to our setup by proving that it is optimal to adopt a modulated barrier strategy at certain positive regime-dependent levels and that the value function can be explicitly characterized as the fixed point of a contraction.

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“…For an overview, the interested reader may consult Schmidli [26], Albrecher and Thonhauser [1], or Avanzi [3]. Two recent papers, Jiang and Pistorius [15], and Sotomayor and Cadenillas [28] deal with the dividend problem under a changing economic environment, described by parameters driven by an observable Markov chain. However these models still assume full information and therefore differ from the model studied here.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Dividend Optimization and Finite Time Ruin Probabilities

Leobacher¹,

Szölgyenyi²,

Thonhauser³

2014

Stochastic Models

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We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We state a numerical procedure for approximating both the optimal dividend strategy and the corresponding value function. Furthermore, threshold strategies are discussed in some detail. Finally, we calculate the probability of ruin in the uncontrolled and controlled situation

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Classical and singular stochastic control for the optimal dividend policy when there is regime switching

Cited by 54 publications

References 32 publications

On optimal dividend strategies in insurance with a random time horizon

On optimal dividend strategies in insurance with a random time horizon

Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching

Bayesian Dividend Optimization and Finite Time Ruin Probabilities

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