Uniform asymptotics for the finite-time and infinite-time ruin probabilities in a dependent risk model with constant interest rate and heavy-tailed claims

Yang, Yang; Wang, Kaiyong

doi:10.1007/s10986-012-9159-3

Cited by 6 publications

(2 citation statements)

References 29 publications

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“…The first norm in (27) is bounded by exp{ 1 8 u ij [ I wi − I + I −wi − I ]} exp{1/2}. The total variation norm is invariant with respect to scale.…”

Section: Proofs For Sums Of Independent Rvsmentioning

confidence: 99%

On closeness of two discrete weighted sums

Čekanavičius¹,

Vellaisamy²

2018

Modern Stochastics: Theory and Applications

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The effect that weighted summands have on each other in approximations of S = w1S1 + w2S2 + · · · + wN SN is investigated. Here, Si's are sums of integer-valued random variables, and wi denote weights, i = 1, . . . , N . Two cases are considered: the general case of independent random variables when their closeness is ensured by the matching of factorial moments and the case when the Si has the Markov Binomial distribution. The Kolmogorov metric is used to estimate the accuracy of approximation.

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“…The first norm in (27) is bounded by exp{ 1 8 u ij [ I wi − I + I −wi − I ]} exp{1/2}. The total variation norm is invariant with respect to scale.…”

Section: Proofs For Sums Of Independent Rvsmentioning

confidence: 99%

On closeness of two discrete weighted sums

Čekanavičius¹,

Vellaisamy²

2018

Modern Stochastics: Theory and Applications

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“…Hence, the first direction is to assume that {N(t) : t ≥ 0} is a renewal process or a generalized renewal process, in which the inter arrival times θ k , k = 1, 2, • • • have a common distribution, not necessarily be exponential, see Chen and Ng (2007), Wang (2008), Yang and Wang (2010) etc. Another direction is to assume that the claim sizes X k , k = 1, 2, • • • , are dependent r.v.s with a common distribution, see Kong and Zong (2008), Yang and Wang (2012) and Gao et al(2012) etc.…”

Section: Introductionmentioning

confidence: 99%

The finite-time ruin probability of the nonhomogeneous Poisson risk model with conditionally independent subexponential claims

Xu¹,

Cheng²

2017

Preprint

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This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common subexponential distribution. The paper also obtains some asymptotic relations of randomly weighted sums n i=1 θ i X i , in which the weights θ i i = 1, 2, • • • , n are nonnegative random variables which are bounded above and the primary random variables X i , i = 1, 2, • • • , n are conditionally independent and follow subexponential distributions.

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