Some results on ruin probabilities in a two-dimensional risk model

By Wai-Sum Chan, Hailiang Yang, Lianzeng Zhang. 2003

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Dependence properties and bounds for ruin probabilities in multivariate compound risk models (2007, background): “Chan et al. (2003) discussed the ruin probability of the aggregate claim, ψor(u1, . . . , um) and ψsim(u1, . . . , um) for the case where the claim sizes X1,n, ..., Xm,n are independent for any n ≥ 1.”
Multivariate risk model of phase type (2005, methodology): “Our model is the multivariate extension of the model discussed in Chan et al. (2003), also allowing a general dependence structure among various claims, and our dependence analysis yields a simple upper bound for certain ψor(u1, u2).”
On the ruin probabilities of a bidimensional perturbed risk model (2007, background): “Following the recent works of Ambagaspitiya (1998), Cossette and Marceau (2000), Yuen et al. (2002) (2006), Chan et al. (2003), Wang and Yuen (2005), and Cai and Li (2005), we consider a bidimensional insurance risk process perturbed by diffusion, in which the bidimensional surplus process R(t) =…”