On the asymptotic behaviour of Lévy processes, Part I: Subexponential and exponential processes

Albin, J.M.P.; Sunden, Mattias

doi:10.1016/j.spa.2008.02.004

Cited by 44 publications

(52 citation statements)

References 25 publications

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“…Write x + = max x 0 for a real number x. For notational convenience we write x n = x 1 x n as a column vector of n dimensions. for some (or, equivalently, for all) y = 0.…”

Section: Introductionmentioning

confidence: 99%

The Maximum of Randomly Weighted Sums with Long Tails in Insurance and Finance

Chen

Yuen

2011

Stochastic Analysis and Applications

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In risk theory we often encounter stochastic models containing randomly weighted sums. In these sums, each primary real-valued random variable, interpreted as the net loss during a reference period, is associated with a nonnegative random weight, interpreted as the corresponding stochastic discount factor to the origin. Therefore, a weighted sum of m terms, denoted as S w m , represents the stochastic present value of aggregate net losses during the first m periods. Suppose that the primary random variables are independent of each other with long-tailed distributions and are independent of the random weights. We show conditions on the random weights under which the tail probability of max 1≤m≤n S w m -the maximum of the first n weighted sums-is asymptotically equivalent to that of S w n -the last weighted sum.

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“…Write x + = max x 0 for a real number x. For notational convenience we write x n = x 1 x n as a column vector of n dimensions. for some (or, equivalently, for all) y = 0.…”

Section: Introductionmentioning

confidence: 99%

The Maximum of Randomly Weighted Sums with Long Tails in Insurance and Finance

Chen

Yuen

2011

Stochastic Analysis and Applications

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“…The following easy corollary to Theorem 3.1 is used in a crucial manner by Albin and Sundén [1]. COROLLARY 4.1.…”

Section: A Tauberian Results For Infinitely Divisible Distributionsmentioning

confidence: 99%

A Note on the Closure of Convolution Power Mixtures (Random Sums) of Exponential Distributions

Albin

2008

J. Aust. Math. Soc.

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“…Amongst them we can found stationary process [20,21] with application of small set hitting probabilities for Gaussian and Rayleigh processes. Lévy processes, which frequently arise in financial engineering, are studied in [22] . The author of [23] also presents a Poisson clumping heuristic for the estimation of rare event probabilities in continuous time.…”

Section: Analytical Estimationmentioning

confidence: 99%