Stochastic processes in insurance and finance

By Paul Embrechts, Rüdiger Frey, H. Furrer. 2001

724 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/b73b1dcd300f22e093a8cc2cf1640d12a29cecf6

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Citations in the corpus

Risk Minimization with Incomplete Information in a Model for High‐Frequency Data (2000, methodology): “These models are close in spirit to models for aggregated claims in actuarial risk theory (see, e.g., Rolski et al. 1999).”
On the Moments of Aggregate Discounted Claims with Dependence Introduced by a FGM Copula (2011, methodology): “As we only need the first two moments for these exemples, we can use the equations (10) and (16) to determine the loading for the risk and then the loaded premium (see e.g. Rolski et al. (1999) for details on premium pinciples).”
Quantifying Distributional Model Risk via Optimal Transport (2016, neutral): “Despite the simplicity of the model, existing results in the literature do not admit simple methods for the computation of ψ(u, T ) (see Asmussen and Albrecher (2010), Embrechts et al. (1997), Rolski et al. (1999) and references therein for a comprehensive collection of results).”
Tail Asymptotics of the Supremum of a Regenerative Process (2007, background): “Detailed discussions of Cox processes and their impact on risk theory can be found in [15], [24], [5], [25], and [3].”
Modeling and Generating Dependent Risk Processes for IRM and DFA (2004, background): “[27]) is described by a counting process ( ) { 0 N t t ≥ } and a family { n Z n∈ } of independent non-negative random variables (claims), independent also of ( ) { 0 .”
Compound geometric residual lifetime distributions and the deficit at ruin (2002, methodology): “It is of interest to consider the residual tail of the compound geometric distribution, namely, x(y) = G(x+ y) G(x) ; y 0: (2.8) The following result for x(y) holds.”
On the discounted penalty function in the renewal risk model with general interclaim times (2007, methodology): “The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed.”
On a risk model with dependence between interclaim arrivals and claim sizes (2006, methodology): “…at ruin, the surplus just prior to ruin and the claim size causing ruin have been extensively studied in these two risk models (see Dufresne and Gerber (1988), Grandell (1991), Dickson (1992, 1993), Gerber and Shiu (1997), Dickson and Hipp (1998), Rolski et al. (1999) and references therein).”
The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion (2003, background): “Some particular forms of this type of equations frequently appear in probability theory and risk theory (see Feller, 1971; Gerber, 1979; Grandell, 1991; Embrechts et al., 1997; Rolski et al., 1999; Gerber and Landry, 1998; Asmussen, 2000).”
Asymptotics of ruin probabilities for controlled risk processes in the small claims case (2004, background): “that MY (R)B for R 0 defined below, and the Cramér condition M? y(R)B : This is for instance fulfilled if there is r such that limr r MY (r) : These conditions are exactly the conditions needed for c(u) Ce Ru in the classical risk model, see [12].”
Randomized observation periods for the compound Poisson risk model: the discounted penalty function (2013, background): “[14]) can be applied for V(x; b) and states that”
The discrete Lindley distribution: properties and applications (2011, background): “Proof By assuming that the claim amount follows an exponential distribution with parameter γ > 0, the nth fold convolution of exponential distribution has a closed form and it is given by [13,17]”