Precise large deviations of aggregate claims in a risk model with regression-type size-dependence

The exponential moment tail of inhomogeneous renewal process

“…(1.3) Chen and Yuen (2012) and Lu (2011) used this assertion considering the large deviation problem, whereas Chen et al (2010), Bi and Zhang (2013), and Wang et al (2012) obtained analogous assertions when the generating random variables θ 1 , θ 2 , . .…”

Web renewal counting processes and their applications in insurance

“…In fact, the above proof implies that Theorem 1(i) in Kočetova et al [ 12 ] and Lemma 3.3 in Bi and Zhang [ 2 ] are direct corollaries of Theorem 2.2 .…”

“…Theorem 2.2 is an extension to the Lemma 3.3 in Bi and Zhang [ 2 ], which is a key lemma in the proof of their main results.…”

“…The precise large deviation of random sums has been extensively investigated in much literature since it was initiated by Klüppelberg and Mikosch [ 11 ], for example, Kaas and Tang [ 10 ], Tang [ 27 ], Lin [ 17 ], Baltrūnas et al [ 1 ], Chen and Zhang [ 5 ], Liu [ 18 ], Li et al [ 15 ], Chen and Yuen [ 4 ], Bi and Zhang [ 2 ], Shen et al [ 25 ], Yang and Sha [ 30 ], Guo et al [ 8 ], Hua et al [ 9 ] and Liu et al [ 20 ], among many others.…”

Large deviations for the discounted aggregate claims in time-dependent risk model with constant interest force

“…Theorem 1.2. Consider the discounted aggregate claims up to time t described by (2). If the conditions of Theorem 1.1 are true, then for every fixed…”