Monte Carlo Simulation of the Moments of a Copula-Dependent Risk Process with Weibull Interwaiting Time

Sharifah Farah Syed Yusoff Alhabshi, Zamira Hasanah Zamzuri and Siti Norafidah Mohd Ramli
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Sharifah Farah Syed Yusoff Alhabshi: Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bandar Baru Bangi 43600, Selangor, Malaysia
Zamira Hasanah Zamzuri: Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bandar Baru Bangi 43600, Selangor, Malaysia
Siti Norafidah Mohd Ramli: Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bandar Baru Bangi 43600, Selangor, Malaysia

Risks, 2021, vol. 9, issue 6, 1-21

Abstract: The widely used Poisson count process in insurance claims modeling is no longer valid if the claims occurrences exhibit dispersion. In this paper, we consider the aggregate discounted claims of an insurance risk portfolio under Weibull counting process to allow for dispersed datasets. A copula is used to define the dependence structure between the interwaiting time and its subsequent claims amount. We use a Monte Carlo simulation to compute the higher-order moments of the risk portfolio, the premiums and the value-at-risk based on the New Zealand catastrophe historical data. The simulation outcomes under the negative dependence parameter ? , shows the highest value of moments when claims experience exhibit overdispersion. Conversely, the underdispersed scenario yields the highest value of moments when ? is positive. These results lead to higher premiums being charged and more capital requirements to be set aside to cope with unfavorable events borne by the insurers.

Keywords: aggregate discounted claims; overdispersed counting process; value-at-risk; solvency capital requirement; premium principle (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
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