Multivariate risk model of phase type

Cai, Jun; Li, Haijun

doi:10.1016/j.insmatheco.2004.11.004

Cited by 65 publications

(56 citation statements)

References 20 publications

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“…Then the MPH of Kulkarni [20] can be recovered from our model by letting the "rewards" U h , h ∈ C follow exponential distributions. For applications of MPH distribution in insurance and risk management, we refer to, e.g., Cai and Li [4]. Furthermore, the CMPH distribution is related to the multivariate Erlang mixture distribution introduced by Lee and Lin [21].…”

Section: Examplementioning

confidence: 99%

CMPH: a multivariate phase-type aggregate loss distribution

Ren

Zitikis

2017

Dependence Modeling

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Abstract:We introduce a compound multivariate distribution designed for modeling insurance losses arising from di erent risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses. We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of di erent loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.

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Section: Examplementioning

confidence: 99%

CMPH: a multivariate phase-type aggregate loss distribution

Ren

Zitikis

2017

Dependence Modeling

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“…Exact solutions of these probabilities are rarely available, and existing result are mostly in the form of bounds. Chan et al(2003) , Cai and Li(2005) and Yuen et al(2006) derived bounds for the ultimate ruin probability Ψ min (u 1 , u 2 ).…”

Section: Bounds For Ruin Probabilitymentioning

confidence: 99%

Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis

Jose¹,

Jacob²

2016

Preprint

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In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-differential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms, where one of the initial capitals is fixed at zero.

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“…These prominently include copulas (e.g., Frees and Valdez [11]), multivariate distributions such as elliptical (e.g., Landsman and Valdez [12]), exponential dispersion (e.g., Landsman and Valdez [13]), Erlang mixtures (e.g., Lee and Lin [14]), Tweedie (e.g., Furman and Landsman [15]), phase-type (e.g., Cai and Li [16]), multivariate Gamma (e.g., Furman [17], Furman and Landsman [18]), Pareto (e.g., Asimit et al [19], Chiragiev and Landsman [20], Vernic [21]). Certainly, we have mentioned here only a few references, but they lead to other important references.…”

Section: Motivationmentioning

confidence: 99%

Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-Ii Model

2013

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This is the published version of the paper.This version of the publication may differ from the final published version. Abstract: Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive model for multi-losses whose dependence and tail heaviness are influenced by a heavy-tailed background risk. A particular attention is given to the distortion and weighted risk measures and allocations, as well as their special cases such as the conditional layer expectation, tail value at risk, and the truncated tail value at risk. We derive formulas that are either of closed form or follow well-defined recursive procedures. In either case, their computational use is straightforward. Permanent repository link

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Multivariate risk model of phase type

Cited by 65 publications

References 20 publications

CMPH: a multivariate phase-type aggregate loss distribution

CMPH: a multivariate phase-type aggregate loss distribution

Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis

Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-Ii Model

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