TY - JOUR

T1 - Capital allocation for a sum of dependent compound mixed poisson variables

T2 - A recursive algorithm approach

AU - Kim, Joseph H. T.

AU - Jang, Jiwook

AU - Pyun, Chaehyun

PY - 2019

Y1 - 2019

N2 - The sum of independent compound Poisson random variables is a widely used stochastic model in many economic applications, including non-life insurance, credit and operational risk management, and environmental sciences. In this article we generalize this model by introducing dependence among Poisson frequency variables through a latent random variable in a linear fashion, which can be translated as a common underlying risk factors affecting the frequencies of individual compound Poisson variables. Despite its natural interpretation, this generalization leads to a highly complicated model with no closed-form distribution function. For this dependent compound mixed Poisson sum with an arbitrary severity distribution, we obtain the Laplace transform and further develop a new recursive algorithm to efficiently compute the probability mass function, extending the well-known Panjer recursion. Furthermore, based on this recursion, we derive another recursive scheme to determine the capital allocation associated with the Conditional Tail Expectation, a popular risk management exercise. A numerical example is presented for the illustration of our findings.

AB - The sum of independent compound Poisson random variables is a widely used stochastic model in many economic applications, including non-life insurance, credit and operational risk management, and environmental sciences. In this article we generalize this model by introducing dependence among Poisson frequency variables through a latent random variable in a linear fashion, which can be translated as a common underlying risk factors affecting the frequencies of individual compound Poisson variables. Despite its natural interpretation, this generalization leads to a highly complicated model with no closed-form distribution function. For this dependent compound mixed Poisson sum with an arbitrary severity distribution, we obtain the Laplace transform and further develop a new recursive algorithm to efficiently compute the probability mass function, extending the well-known Panjer recursion. Furthermore, based on this recursion, we derive another recursive scheme to determine the capital allocation associated with the Conditional Tail Expectation, a popular risk management exercise. A numerical example is presented for the illustration of our findings.

UR - http://www.scopus.com/inward/record.url?scp=85061279857&partnerID=8YFLogxK

U2 - 10.1080/10920277.2018.1506705

DO - 10.1080/10920277.2018.1506705

M3 - Article

SN - 1092-0277

VL - 23

SP - 82

EP - 97

JO - North American Actuarial Journal

JF - North American Actuarial Journal

IS - 1

ER -