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

Cai, Jun; Feng, Runhuan; Willmot, Gordon E.

doi:10.1017/s0001867800003396

Cited by 21 publications

(29 citation statements)

References 28 publications

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“…Applications and properties of T s operator can be found in [7], [8], and [24], among others. For simplicity, we define an operator T s f (x) for an integrable function f and for s ∈ R, by…”

Section: An Integral Operatormentioning

confidence: 99%

Extension of the past lifetime and its connection to the cumulative entropy

Crescenzo

Toomaj

2015

J. Appl. Probab.

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Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and series systems under suitably proportionality assumptions on the hazards rates. Furthermore, we prove that the (reversed) relevation transform is commutative if and only if the proportional (reversed) hazard rate model holds. By repeated application of the reversed relevation transform we construct a decreasing sequence of random variables which leads to new weighted probability densities. We obtain various relations involving ageing notions and stochastic orders. We also exploit the connection of such a sequence to the cumulative entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative formulae for computing the mean and the cumulative entropy of the random variables of the sequence are finally investigated.

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Section: An Integral Operatormentioning

confidence: 99%

Extension of the past lifetime and its connection to the cumulative entropy

Crescenzo

Toomaj

2015

J. Appl. Probab.

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“…Cost functions of the form (1), or more generally involving a running costs function l(X t ), are also studied by Cai et al (2009) in an uncontrolled piecewise-deterministic compound Poisson environment. The structure of the manuscript is as follows.…”

Section: Introductionmentioning

confidence: 99%

An optimal reinsurance problem in the Cramér–Lundberg model

Cani

Thonhauser

2016

Math Meth Oper Res

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In this article we consider the surplus process of an insurance company within the Cramér-Lundberg framework with the intention of controlling its performance by means of dynamic reinsurance. Our aim is to find a general dynamic reinsurance strategy that maximizes the expected discounted surplus level integrated over time. Using analytical methods we identify the value function as a particular solution to the associated Hamilton-Jacobi-Bellman equation. This approach leads to an implementable numerical method for approximating the value function and optimal reinsurance strategy. Furthermore we give some examples illustrating the applicability of this method for proportional and XL-reinsurance treaties.

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“…(2009) and Chapter 8 of Asmussen and Albrecher (2010), where some well-known important risk models are given by taking different kinds of functions of .…”

Section: Introductionmentioning

confidence: 99%

The distribution of some extremum on the risk process whose income depend on the current reserve

Liu

Zhang

2016

SpringerPlus

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This paper considers the distribution of some extremum on the risk process whose income depend on the current reserve. We first construct the defective renewal sequence and obtain the density function of them. By the presented renewal measure and the strong Markov property, the distribution of the first hitting time is obtained explicitly. Then, the ruin probability and the probability that the surplus process less than x is obtained. Furthermore, the distribution of supreme profits before ruin, the joint distributions of the supreme profit and the deficit before the time of the surplus process first up-crossing level zero after ruin, and the joint distributions of the supreme profit and the deficit before the surplus process leave zero ultimately are derived. Finally, the exact calculating results for them are obtained when the individual claim amounts in the compound Poisson risk model are exponentially distributed.

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

Cited by 21 publications

References 28 publications

Extension of the past lifetime and its connection to the cumulative entropy

Extension of the past lifetime and its connection to the cumulative entropy

An optimal reinsurance problem in the Cramér–Lundberg model

The distribution of some extremum on the risk process whose income depend on the current reserve

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