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# Asymptotic estimates for finite-time ruin probabilities in a generalized dependent bidimensional risk model with CMC simulations

• *Corresponding author: Dongya Cheng

The fourth author is supported by National Natural Science Foundation of China (No. 11401415)

• This paper studies ruin probabilities of a generalized bidimensional risk model with dependent and heavy-tailed claims and additional net loss processes. When the claim sizes have long-tailed and dominated-varying-tailed distributions, precise asymptotic formulae for two kinds of finite-time ruin probabilities are derived, where the two claim-number processes from different lines of business are almost arbitrarily dependent. Under some extra conditions on the independence relation of claim inter-arrival times, the class of the claim-size distributions is extended to the subexponential distribution class. In order to verify the accuracy of the obtained theoretical result, a simulation study is performed via the crude Monte Carlo method.

Mathematics Subject Classification: Primary: 62P05; Secondary: 62E10.

 Citation:

• Figure 1.  Sample paths of the two discounted values of the surplus processes $R_1(t)$ (the blue lines) and $R_2(t)$ (the orange lines) (obtained based on $0\le t\le50$, $(x, y) = (20, 20)$, $r = 0.03$ and $c = 50$)

Table 1.  Results of simulations

 x y $\frac{N_{\text{sim}}}{N}$ $\frac{N_{\text{and}}}{N}$ $R_T(x, y)$ $E_{\text{sim}}$ $E_{\text{and}}$ $1000$ $1000$ $1.50\times 10^{-5}$ $1.54\times 10^{-5}$ $1.5222\times 10^{-5}$ $0.01458$ $-0.01169$ $1500$ $1500$ $7.10\times 10^{-6}$ $7.30\times 10^{-6}$ $6.7656\times 10^{-6}$ $-0.04943$ $-0.07899$ $2000$ $2000$ $3.90\times 10^{-6}$ $4.00\times 10^{-6}$ $3.8056\times 10^{-6}$ $-0.02481$ $-0.05108$ $2500$ $2500$ $2.50\times 10^{-6}$ $2.60\times 10^{-6}$ $2.4360\times 10^{-6}$ $-0.02627$ $-0.06732$ $3000$ $3000$ $1.70\times 10^{-6}$ $1.80\times 10^{-6}$ $1.6914\times 10^{-6}$ $-0.00508$ $-0.06421$
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