The compound Poisson risk model with multiple thresholds

Lin, Xiaodong; Sendova, Kristina P.

doi:10.1016/j.insmatheco.2007.06.008

Cited by 63 publications

(35 citation statements)

References 13 publications

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“…. , α n < c for corresponding thresholds respectively (see Lin and Pavlova (2006) and Lin and Sendova (2008)), it can be easily shown that the corresponding function…”

Section: Piecewise-deterministic Compound Poisson Processmentioning

confidence: 99%

On the expectation of total discounted operating costs up to default and its applications

2009

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In this paper we first consider the expectation of the total discounted claim costs up to the time of ruin, and then, more generally, we study the expectation of the total discounted operating costs up to the time of default, which is the first passage time of a surplus process downcrossing a given level. These two quantities include the expected discounted penalty function at ruin or the Gerber-Shiu function, the expected total discounted dividends up to ruin, and other interesting quantities as special cases among a class of risk processes. As an illustration, we consider a piecewise-deterministic compound Poisson risk model. This model recovers many risk models appearing in the literature such as the compound Poisson risk models with interest, absolute ruin, dividends, multiple thresholds, and their dual models. We derive and solve the integro-differential equation for the expected present value of the total discounted operating costs up to default. The solutions to the expected present value of the total discounted operating costs up to default can be used as a unified approach to solving many ruin-related quantities. As applications, we derive explicit solutions for the expected accumulated utility up to ruin, the absolute ruin probability with varying borrowing rates, the expected total discounted claim costs up to ruin, the Gerber-Shiu function with two-sided jumps, and the price for a perpetual American put option with two-sided jumps.

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“…. , α n < c for corresponding thresholds respectively (see Lin and Pavlova (2006) and Lin and Sendova (2008)), it can be easily shown that the corresponding function…”

Section: Piecewise-deterministic Compound Poisson Processmentioning

confidence: 99%

On the expectation of total discounted operating costs up to default and its applications

2009

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“…For example, it is arguably desirable for dividend strategies to distribute more dividends as surplus reaches high levels and one example of such strategies is known as multilayer dividend strategies (see, e.g., Albrecher and Hartinger [46], Lin and Sendova [47]). For example, dividend payments at time t is given by…”

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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“…We adopt a similar method used in Gerber and Shiu (2005) and Lin and Sendova (2008). For j = 0, 1, .…”

Section: )mentioning

confidence: 99%

Gerber–Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

Yang

Zhang

2008

Insurance: Mathematics and Economics

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The compound Poisson risk model with multiple thresholds

Cited by 63 publications

References 13 publications

On the expectation of total discounted operating costs up to default and its applications

On the expectation of total discounted operating costs up to default and its applications

A Note on Realistic Dividends in Actuarial Surplus Models

Gerber–Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

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