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doi: 10.3934/jimo.2021022
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## Asymptotics for VaR and CTE of total aggregate losses in a bivariate operational risk cell model

 1 Department of Mathematical Sciences, Xi'an Jiaotong Liverpool University, Suzhou, Jiangsu 215123, China 2 School of Mathematics and Statistics, Nanjing Audit University, Nanjing, Jiangsu 211815, China

* Corresponding author: Yang Yang

Received  July 2020 Revised  October 2020 Early access January 2021

This paper considers a bivariate operational risk cell model, in which the loss severities are modelled by some heavy-tailed and weakly (or strongly) dependent nonnegative random variables, and the frequency processes are described by two arbitrarily dependent general counting processes. In such a model, we establish some asymptotic formulas for the Value-at-Risk and Conditional Tail Expectation of the total aggregate loss. Some simulation studies are also conducted to check the accuracy of the obtained theoretical results via the Monte Carlo method.

Citation: Yishan Gong, Yang Yang. Asymptotics for VaR and CTE of total aggregate losses in a bivariate operational risk cell model. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021022
##### References:

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##### References:
Comparison of the simulated and asymptotic estimates for $\mathrm{VaR}_q(S(t))$, with Frank dependent and Weibull distributed severities and AI or AD dependent frequency processes in Theorem 3.1
Comparison of the simulated and asymptotic estimates for $\mathrm{VaR}_q(S(t))$, with Frank dependent and Pareto distributed severities and AI or AD dependent frequency processes in Theorem 3.2
Comparison of the simulated and asymptotic estimates for $\mathrm{CTE}_q(S(t))$, with Frank dependent and Pareto distributed severities and AI or AD dependent frequency processes in Theorem 3.2
Comparison of the simulated and asymptotic estimates for $\mathrm{VaR}_q(S(t))$, with Gumbel dependent and Pareto distributed severities and AI or AD dependent frequency processes in Theorem 3.3
Comparison of the simulated and asymptotic estimates for $\mathrm{CTE}_q(S(t))$, with Gumbel dependent and Pareto distributed severities and AI or AD dependent frequency processes in Theorem 3.3
Comparison of the simulated and asymptotic estimates for $\mathrm{VaR}_q(S(t))$, with common frequency process, and Gumbel or Frank dependent Pareto distributed severities in Theorems 3.2 and 3.3
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