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On ruin for the Erlang(n) risk process
Abstract A defective renewal equation is derived for the expected discounted penalty due at ruin, φ δ (u)=E[ e −δT w(U(T − ),|U(T)|)I(T in a risk model with Erlang(n) claim inter-arrival times. TheExpand
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On a class of renewal risk models with a constant dividend barrier
Abstract We consider a compound renewal (Sparre Andersen) risk process in the presence of a constant dividend barrier in which the claim waiting times are generalized Erlang( n ) distributed (i.e.,Expand
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On a general class of renewal risk process: analysis of the Gerber-Shiu function
We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a K n distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials ofExpand
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The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion
We consider a Sparre Andersen risk process that is perturbed by an independent diffusion process, in which claim inter-arrival times have a generalized Erlang(n) distribution (i.e. as the sum of nExpand
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On The Expected Discounted Penalty function for Lévy Risk Processes
Abstract Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such a model is either a compound Poisson process itself or a process with anExpand
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Ruin Probabilities for Two Classes of Risk Processes
We consider a risk model with two independent classes of insurance risks. We assume that the two independent claim counting processes are, respectively, Poisson and Sparre Andersen processes withExpand
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Extending pricing rules with general risk functions
TLDR
The paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging strategy is measured by a general risk function, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. Expand
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Generalized linear models for dependent frequency and severity of insurance claims
Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this oft unwarranted assumption can be relaxed in a simple way while incorporatingExpand
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Fourier Inversion Formulas in Option Pricing and Insurance
Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 0) also arises in excess-of-loss or stop-lossExpand
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Moments of compound renewal sums with discounted claims
Abstract Delbaen and Haezendonck [Ins. Math. Econ. 6 (1987) 85] and Willmot [Scand. Actuarial J. 1 (1989) 1] give an analytical expression for the net premium density of a compound Poisson presentExpand
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