Stability of perpetuities

By C. Goldie, Ross Maller. 2000

171 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b4e3d9334a9b2391296d6ab14fa74fad26d1f7b

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Citations in the corpus

Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)-Processes (2009, background): “For the converse, we cite the following result: Proposition 1 (Goldie and Maller (2000), Theorem 2.1) Let d = 1 and (At, Bt)t∈Z be i.i.d. in R × R. Suppose that P (B0 = 0) 1, P (A0 = 0) = 0, that ∏n i=0A−i converges almost surely to zero as n → ∞, and that ∫ (1,∞) log q TA(log q) P|B0|(dq) ∞,…”
GARCH modelling in continuous time for irregularly spaced time series data (2008, unknown): “[8, 21]) to get the explicit representation”
Stability and the Lyapounov exponent of threshold AR-ARCH Models (2004, unknown): “Under the given assumptions, the necessary and sufficient condition for {Yt} to have a stationary solution is γ 0 [Brandt (1986), Bougerol and Picard (1992a), Theorem 2.5, and Goldie and Maller (2000)].”
Tail asymptotics for exponential function-als of L evy processes (2006, unknown): “According to Theorem 2.1 of Goldie and Maller [19] (in particular Condition (2.3) The condition X ( u ) → ∞ a.s. is equivalent to the a.s. existence of some u ε such that e − X ( u ) < ε for u > u ε , ε > 0.”
On Distributional Properties of Perpetuities (2008, background): “As to the last problem, Goldie and Maller [10] gave the following complete characterization of the a.”
Generalised Ornstein-Uhlenbeck Processes and the Convergence of Levy Integrals (2005, background): “or similar, so direct application of the results of [ 19 ] would give uncheckable conditions phrased in terms of the marginal distributions of these components, which are quite inaccessible.”
The tail of the stationary distribution of a random coefficient AR(q) model (2004, unknown): “ and An = α 1n ··· αqn Iq−1 0 (1.6) , n∈N, where Iq−1 denotes the identity matrix of order q−1. Standard conditions for the existence of a stationary solution to (1.4) are given in [15] (see also [11]) and require that (1.7) Elog+ |A 1|<∞ and Elog+ |ζ 1|<∞ and that the top Lyapunov exponent ”
Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, background): “Recall that t > 0 is fixed and denote by G = (Gs)0≤s≤t the smallest filtration containing (Fs)0≤s≤t and such that (ξt, ηt) is G0-measurable.”
Integrated insurance risk models with exponential Lévy investment (2008, background): “For the sequence (Vθ,k)k∈N0 Goldie and Maller [8] derive also for this discrete time process NASCs for stationarity; see their Theorem 2.1.”
Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models (2012, unknown): “Actually, Klüppelberg, Lindner, and Maller (2004) (see also Goldie and Maller (2000)) showed that when γ0 = 0 ht → ∞ in probability(1.6) instead of almost surely in the case γ0 > 0.3 The astonishing difficulties encountered in the case γ0 = 0 are related to the fact that the sequence ht = ht t +…”
A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks (2008, background): “We also provide a necessary and sufficient condition for uniform integrability of these martingales in the most general situation which particularly means that the classical (LlogL)-condition is not always needed.”
Ornstein–Uhlenbeck Processes and Extensions (2009, background): “The remaining Lévy processes, that is, Lévy processes with “finite activity”, are compound Poisson processes (possibly with a drift).”
Estimation in nonstationary random coefficient autoregressive models (2009, background): “Since (9) implies Pfu þ b0 ¼ 0g ¼ 0, the result follows immediately from Remark 2.8 and Cor. 4.1 of Goldie and Maller (2000). u We start with the study of the log-likelihood function.”
ON MARKOV-SWITCHING ARMA PROCESSES—STATIONARITY, EXISTENCE OF MOMENTS, AND GEOMETRIC ERGODICITY (2009, background): “sequence, the results of Bougerol & Picard (1992) show under technical conditions that the strict negativity of the Lyapunov coefficient is also necessary for the existence of a causal solution to an MS-ARMA equation. Confer also Goldie & Maller (2000)”
Elementary fixed points of the BRW smoothing transforms with infinite number of summands (2003, methodology): “That the conditions (a)-(c) and (d)-(e) are equivalent follows from Theorem 2.1 and Corollary 4.1 of Goldie and Maller (2000).”