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Table 4 Comparison of Lundberg exponent: exponential case. \((\theta _{1}, \theta_{1}^{R})=(0.2, 0.4)\) and \((\theta_{2}, \theta_{2}^{R})= (0.25, 0.5)\), 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

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

2.151698

2.245443

2.223645

2.134013

2.03478

2.012961

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

2.592899

2.663988

2.731697

2.735907

2.641812

2.4257

\(R^{*}\)

0.1564

0.1368

0.1303

0.1323

0.1431

0.1672

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

0.209349

0.254557

0.271713

0.266337

0.239386

0.18796

\(R^{*} \)

0.162025

0.139998

0.135537

0.137071

0.148071

0.169951

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

0.1978

0.2466

0.2579

0.2539

0.2275

0.1828