Capital Allocation for a Sum of Dependent Compound Mixed Poisson Variables: A Recursive Algorithm Approach

Joseph H.T. Kim, Jiwook Jang, Chaehyun Pyun

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)82-97
Number of pages16
JournalNorth American Actuarial Journal
Volume23
Issue number1
DOIs
Publication statusPublished - 2019 Jan 2

Fingerprint

Compound Poisson
Recursive Algorithm
Risk Management
Recursion
Siméon Denis Poisson
Random variable
Operational Risk
Credit Risk
Common factor
Dependent
Latent Variables
Risk Factors
Insurance
Laplace transform
Exercise
Stochastic Model
Tail
Distribution Function
Closed-form
Economics

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

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Capital Allocation for a Sum of Dependent Compound Mixed Poisson Variables : A Recursive Algorithm Approach. / Kim, Joseph H.T.; Jang, Jiwook; Pyun, Chaehyun.

In: North American Actuarial Journal, Vol. 23, No. 1, 02.01.2019, p. 82-97.

Research output: Contribution to journalArticle

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