On the nth stop-loss transform order of ruin probability

Stationary-excess operator and convex stochastic orders

“…see, e.g., Cheng and Pai (2003). Indeed, considering the iterated right-tail distribution functions of X, i.e.F 1 (X, x) = P (X > x) and…”

On the stop-loss transform and order for the surplus process perturbed by diffusion

“…(2.8) and Proposition 1 generalize Theorem 1.3 and Theorem 1.4 of Cheng and Pai (2003), respectively, where both δ and D are zero.…”

“…n k=0 v k . See Hesselager et al (1998) and Cheng and Pai (2003) for more details. Lin and Willmot (1999) …”

“…With the definition of Ω , Cheng and Pai (2003) generalized Definition 2 to Definition 3. Suppose Q 1 , Q 2 ∈ Ω and the nth stop-loss transforms of Q 1 and Q 2 exist.…”

“…Goovaerts et al (1984Goovaerts et al ( , 1990, Kaas et al (1994), Kaas and Hesselager (1995) and Hürlimann (2000) studied the higher degree stop-loss transform and order. Cheng and Pai (2003) extended the concept of the higher degree stop-loss transform and order to a family of non-negative monotone decreasing functions to obtain a result relating the stop-loss ordering of ruin probabilities for the classical continuous time surplus process to the stop-loss ordering of the claim size random variable. This paper extends the results obtained in Cheng and Pai (2003) to ones based on the surplus process perturbed by diffusion.…”