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(15 citation statements)

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“…Our orthogonal polynomial method involves the standard integer moment sequence for S N , in contrast to more exotic types of moments used by some recent methods. Gzyl and Tagliani [16] uses the fractional moments within a max-entropic based method, while Mnatsakanov and Sarkisian [26] performs an inversion of the scaled Laplace transform via the exponential moments. In addition to proposing an approximation for the survival function of S N , we provide an efficient way to compute the usual slp (1) for reinsurance applications.…”

confidence: 99%

“…Our orthogonal polynomial method involves the standard integer moment sequence for S N , in contrast to more exotic types of moments used by some recent methods. Gzyl and Tagliani [16] uses the fractional moments within a max-entropic based method, while Mnatsakanov and Sarkisian [26] performs an inversion of the scaled Laplace transform via the exponential moments. In addition to proposing an approximation for the survival function of S N , we provide an efficient way to compute the usual slp (1) for reinsurance applications.…”

confidence: 99%

“…In this case, the probability P * solving (11) has density ρ * (ξ) given by (12), and S Q (P * ) = Σ(λ * , µ).…”

confidence: 99%

“…Suppose that a random variable X distributed according to F. Assume also that we are given the sequence μ(F) = {μ t (F), t ∈ ℕ α } defined by the values of the scaled Laplace transform of F: (1) To simplify the notations let us assume in (1) that the scale value c = In b for some 1 < b ≤ exp (1). The problem of the optimal choice of the parameter b represents another question addressed in this article.…”

confidence: 99%

“…Unfortunately, the closed form solutions for many such cases are not available. See for example, Gzyl and Tagliani [1] and the references therein. Also, the problem of decompounding the random sums represents another interesting and difficult probabilistic inverse problem.…”

confidence: 99%