On the first time of ruin in the bivariate compound Poisson model

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Asymptotics for a bidimensional risk model with two geometric Lévy price processes (2019, methodology): “[26] considered a bidimensional compound Poisson risk model with R1(t) = R2(t) = 0 for all t ≥ 0 and a constant premium rate c > 0, and discussed various methods for evaluation of finite-time ruin probability.”
Optimal proportional reinsurance with common shock dependence (2015, background): “Although research on risk models with dependent risk is increasing rapidly in recent years (see, for example, Wang (1998), Yuen et al. (2002, 2006), and the references therein), very few of these contributions deal with the problem in relation to optimal reinsurance.”
Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims (2011, methodology): “[17] considered two dependent classes of insurance business using the so-called two-dimensional compound Poisson risk model, and discussed various methods for evaluation of ruin probabilities.”