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Table 3 Comparison of Lundberg exponent: Pareto distribution. \((\theta_{1}, \theta_{1}^{R})=(\theta_{2}, \theta_{2}^{R})= (0.2, 0.4)\), values of Lundberg exponent and upper bound of ruin probability with different dependence parameters for Hu’s model and our model

From: Minimizing Lundberg inequality for ruin probability under correlated risk model by investment and reinsurance

\((\alpha_{11},\alpha_{12})\)

(0,1)

(0.2,0,8)

(0.4,0.6)

(0.6,0.4)

(0.8,0.2)

(1,0)

\((\alpha_{21},\alpha_{22})\)

(1,0)

(0.8,0.2)

(0.6,0.4)

(0.4,0.6)

(0.2,0.8)

(0,1)

\((\lambda_{1},\lambda_{2})\)

(4,2)

(3.6,2.4)

(3.2,2.8)

(2.8,3.2)

(2.4,3.6)

(2,4)

ρ

0

0.111111

0.160714

0.160714

0.111111

0

\(M^{*}_{1}\)

2.325091

2.485092

2.521622

2.470896

2.380495

2.325091

\(M^{*}_{2} \)

2.325091

2.380495

2.470896

2.521622

2.485092

2.325091

\(R_{H}^{*} \)

0.144713

0.125136

0.117427

0.117427

0.125136

0.144713

\(e^{-10R_{H}^{*}} \)

0.2352

0.2861

0.3090

0.3090

0.2861

0.2352

\(R^{*} \)

0.160045

0.132486

0.120324

0.120011

0.127033

0.145129

\(e^{-10R^{*}}\)

0.2018

0.2658

0.3002

0.3012

0.2807

0.2343