The moments of the time of ruin, the surplus before ruin, and the deficit at ruin

By X.Sheldon Lin, Gordon E. Willmot. 2000

163 citations recorded by the source corpus.

Subfields: Demography, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/166f3fd0c4196b340e4dbc7971022f1e661bbfa6

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Citations in the corpus

Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process (2007, methodology): “Lin and Willmot (2000) and Lin et al. (2003) computed objects such as Ex(e −µσa (Yσa − a)n), (8) where, in particular, combinations of exponentials and mixtures of Erlang distributions are considered for the jump distribution in the classical Cramér–Lundberg model.”
Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process (2003, background): “Lin and Willmot (2000) derived explicit expressions for (u) in the compound Poisson model.”
The compound Poisson risk model with a threshold dividend strategy (2006, methodology): “If in addition, we define pn = ∫∞ 0 yndP (y) to be the nth moment of Y1, we can apply formula (2.4) in Lin and Willmot (2000), namely, P e,n(y) = 1 pn ∫ ∞ y (t− y)ndP (t) to find ∫ ∞ u ζ(t)dt = pl ∫ ∞ u thP e,l(t)dt for this particular form of w.”
On the Density and Moments of the Time of Ruin with Exponential Claims (2003, methodology): “In Section 3, we use this pdf to derive explicit expressions for the moments which do not involve recursive calculations of intermediate quantities, as is the case for the formulas in Lin and Willmot (2000).”
On the discounted penalty function in a Markov-dependent risk model (2005, unknown): “(22) This leads to the defective density of the surplus prior to ruin f(y1|x) = λ c− λμ (”
On a class of discrete time renewal risk models (2005, unknown): “Substituting (17) into (16) yields φ̂(s) = k̂(v/s) ω̂(s) − ∑m i=1 θi(1−qi) v bi (s−v qi) [1 − k̂(v/s) p̂(s)] , (18)”
On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier (2005, background): “The discounted penalty function introduced by Gerber and Shiu [13] allows to study properties of the time of ruin, the severity of ruin and the surplus prior to ruin at the same time (for a detailed discussion in the classical risk model without barriers, see [17] and the references therein).”
On the discounted penalty function in the renewal risk model with general interclaim times (2007, methodology): “Moments of the discounted deficit in the classical Poisson model, a special case of the present model, were discussed by Lin and Willmot (2000). 2 Defective renewal equation analysis To begin the analysis, the defective renewal equation approach of Gerber and Shiu (1998, p.”
Compound geometric residual lifetime distributions and the deficit at ruin (2002, background): “See Willmot and Lin (2001, section 11.2), who show that (0) = 1 1 2fcE(W ) E(Y )g c2s1 ; (4.2) and F (y) = R1 0 e s1t P1(y + t)dtR1 0 e s1t P1(t)dt : (4.3) The distribution defined by (4.3) is of the form studied in detail in Lin and Willmot (1999, 2000), but with P replaced by P1.”