Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type

Furman, Edward; Kye, Yisub; Su, Jianxi

doi:10.1016/j.insmatheco.2020.11.007

Cited by 18 publications

(7 citation statements)

References 41 publications

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“…, X M are mutually independent, e.g. [7,54,64,67,65,35]. Some notable exceptions include [73] concerning asymptotic analysis, [8] who assumed X 1 , .…”

Section: Multiplicative Background Risk Model and Its Capital Allocationmentioning

confidence: 99%

Multivariate matrix-exponential affine mixtures and their applications in risk theory

Cheung¹,

Peralta²,

Woo³

2022

Preprint

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In this paper, a class of multivariate matrix-exponential affine mixtures with matrixexponential marginals is proposed. The class is shown to possess various attractive properties such as closure under size-biased Esscher transform, order statistics, residual lifetime and higher order equilibrium distributions. This allows for explicit calculations of various actuarial quantities of interest. The results are applied in a wide range of actuarial problems including multivariate risk measures, aggregate loss, large claims reinsurance, weighted premium calculations and risk capital allocation. Furthermore, a multiplicative background risk model with dependent risks is considered and its capital allocation rules are provided as well. We finalize by discussing a calibration scheme based on complete data and potential avenues of research.

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“…, X M are mutually independent, e.g. [7,54,64,67,65,35]. Some notable exceptions include [73] concerning asymptotic analysis, [8] who assumed X 1 , .…”

Section: Multiplicative Background Risk Model and Its Capital Allocationmentioning

confidence: 99%

Multivariate matrix-exponential affine mixtures and their applications in risk theory

Cheung¹,

Peralta²,

Woo³

2022

Preprint

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“…These multivariate distributions were studied from another perspective in [16], where the authors derived some properties in the context of risk management. We presently derive some probabilistic properties, provide an estimation method, and extend the class to allow for deterministic time transforms.…”

Section: Then the Joint Survival Function Of Y Y Y Is Given Bymentioning

confidence: 99%

Heavy-tailed phase-type distributions: A unified approach

Bladt¹,

Yslas²

2021

Preprint

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Heavy-tailed phase-type random variables have mathematically tractable distributions and are conceptually attractive to model physical phenomena due to their interpretation in terms of a hidden Markov structure. Three recent extensions of regular phase-type distributions give rise to models which allow for heavy tails: discrete-or continuous-scaling; fractional-time semi-Markov extensions; and inhomogeneous time-change of the underlying Markov process. In this paper, we present a unifying theory for heavy-tailed phase-type distributions for which all three approaches are particular cases. Our main objective is to provide useful models for heavy-tailed phase-type distributions, but any other tail behavior is also captured by our specification. We provide relevant new examples and also show how existing approaches are naturally embedded. Subsequently, two multivariate extensions are presented, inspired by the univariate construction which can be considered as a matrix version of a frailty model. We provide fully explicit EM-algorithms for all models and illustrate them using synthetic and real-life data.

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“…For this, we need a few auxiliary notions first. That is, Definitions 1 and 2 below introduce the univariate size-biased transform and its multivariate extension (Arratia et al, 2019;Furman et al, 2020c;Patil and Ord, 1976), both playing major roles in our analysis.…”

Section: General Considerationsmentioning

confidence: 99%

“…We next define the partial size-biased transform, which is a useful special case of the one presented in Definition 2 (e.g., Arratia et al, 2019;Furman et al, 2020c, for a few recent results in which the partial size-biased transform plays a central role but is not explicitly defined).…”

Section: General Considerationsmentioning

confidence: 99%

Some Results on the Risk Capital Allocation Rule Induced by the Conditional Tail Expectation Risk Measure

Mohammed

Furman

2021

SSRN Journal

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Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type

Cited by 18 publications

References 41 publications

Multivariate matrix-exponential affine mixtures and their applications in risk theory

Multivariate matrix-exponential affine mixtures and their applications in risk theory

Heavy-tailed phase-type distributions: A unified approach

Some Results on the Risk Capital Allocation Rule Induced by the Conditional Tail Expectation Risk Measure

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