Randomized observation periods for the compound Poisson risk model: the discounted penalty function

Albrecher, Hansjörg; Cheung, Eric C.K.; Thonhauser, Stefan

doi:10.1080/03461238.2011.624686

Cited by 106 publications

(154 citation statements)

References 19 publications

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“…For solvency purposes, it is more appropriate to view this threshold level as the insurer's solvency capital requirement (SCR) set by the regulatory body. Therefore, new risk concepts and models have recently been introduced: Parisian ruin (see, e.g., [4], [14], [13]), random observations (see, e.g., [1]) and Omega models (see, e.g., [2], [6] and [3]). …”

Section: Introductionmentioning

confidence: 99%

On the Time Spent in the Red by a Refracted Lévy Risk Process

Renaud¹

2014

Journal of Applied Probability

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Abstract. In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the process recovers. The analysis is mainly focused on the time a refracted Lévy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from [10] and [15], we identify the distribution of various functionals related to occupation times of refracted spectrally negative Lévy processes. For example, these results are used to compute the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.

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Section: Introductionmentioning

confidence: 99%

On the Time Spent in the Red by a Refracted Lévy Risk Process

Renaud¹

2014

Journal of Applied Probability

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“…Such a random depletion mechanism with its simple formulas may serve as an approximation of depletion mechanisms at deterministic time points. In fact, if the depletion mechanism according to a homogeneous Poisson process is extended to a renewal process with Erlang-distributed inter-occurrence times, an analysis in the spirit of [3] may still be possible in the present setup. We leave this extension for future research.…”

Section: Resultsmentioning

confidence: 99%

A Queueing Model With Randomized Depletion of Inventory

Albrecher

Boxma²,

Essifi³

et al. 2016

Prob. Eng. Inf. Sci.

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Abstract. In this paper we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.

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“…Some recent papers attempt to simplify the problem by relaxing model assumptions (e.g., Albrecher, Cheung, and Thonhauser [44]) or using techniques such as Erlangisation (e.g., Avanzi, Cheung, Wong, and Woo [45]) to obtain approximations to the solutions. Much work is still required.…”

Section: Implications For Actuarial Surplus Modelsmentioning

confidence: 99%

A Note on Realistic Dividends in Actuarial Surplus Models

Avanzi

Wong

2016

Risks

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Abstract:Because of the profitable nature of risk businesses in the long term, de Finetti suggested that surplus models should allow for cash leakages, as otherwise the surplus would unrealistically grow (on average) to infinity. These leakages were interpreted as 'dividends'. Subsequent literature on actuarial surplus models with dividend distribution has mainly focussed on dividend strategies that either maximise the expected present value of dividends until ruin or lead to a probability of ruin that is less than one (see Albrecher and Thonhauser, Avanzi for reviews). An increasing number of papers are directly interested in modelling dividend policies that are consistent with actual practice in financial markets. In this short note, we review the corporate finance literature with the specific aim of fleshing out properties that dividend strategies should ideally satisfy, if one wants to model behaviour that is consistent with practice.

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Randomized observation periods for the compound Poisson risk model: the discounted penalty function

Cited by 106 publications

References 19 publications

On the Time Spent in the Red by a Refracted Lévy Risk Process

On the Time Spent in the Red by a Refracted Lévy Risk Process

A Queueing Model With Randomized Depletion of Inventory

A Note on Realistic Dividends in Actuarial Surplus Models

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