A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier

By Hans U. Gerber, X. Lin, Hailiang Yang. ASTIN Bulletin: The Journal of the International Actuarial Association, 2006

97 citations recorded by the source corpus.

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Citations in the corpus

The optimal dividend barrier in the Gamma–Omega model (2011, background): “[8], we introduce a function hðxÞ; 1\x\1: It is unique only up to a constant factor and defined by the following property: Let 1\x\y\1: Given the initial surplus x, the expectation of a discounted contingent payment of 1 at the time when the surplus reaches the level y, provided that bankruptcy has ”
Randomized observation periods for the compound Poisson risk model: the discounted penalty function (2013, unknown): “Taking the derivative of Equation (2.1) with respect to h and letting h00, we obtain the system of IDEs 0 ¼ cm0dðxÞ ðkþ cþ dÞmdðxÞ þ cw2ð xÞ þ k Z 1 0 mdðx yÞfY ðyÞ dy; xB0; (2.2) 0 ¼ cm0dðxÞ ðkþ dÞmdðxÞ þ k Z 1 0 mdðx yÞfY ðyÞ dy; x 0: (2.3) A priori, the derivatives above are right-hand…”
Bank Capital, Liquid Reserves, and Insolvency Risk (2017, unknown): “banks is to maintain their Tier 1 leverage ratio in excess of either 4%, 7% or 9% depending their asset base; see Getter (2014). In our analysis we thus consider Tier 1 leverage ratio requirements at Ω = 4%, 7%, and 9% and implement a leverage ratio requirement at Ω = 20% to investigate the effects ”
Randomized Observation Periods for the Compound Poisson Risk Model: Dividends (2011, unknown): “[8]).”
On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes (2008, unknown): “Besides finding the optimal strategy, a large body of literature exists [9, 12, 15, 16, 19, 23, 24, 25, 28, 32, 33] in which expressions are derived for, for example, the expected time of ruin, the moments of the expected paid out dividends and the Gerber–Shiu discounted penalty function, under the ”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “…key papers which pertains to generalizations of the Cramér-Lundberg process includes for example Dickson (1992, 1993); Gerber and Shiu (1997, 1998); Gerber and Landry (1998); Lin and Willmot (1999); Yang and Zhang (2001); Cai and Dickson (2002); Tsai and Willmot (2002); Cai (2004); Garrido and…”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, background): “[21] and Zajic [43]), or continuous payoffs until ruin; see Albrecher and Thonhauser [41], Cai et al.”
Dividend maximization under consideration of the time value of ruin (2007, background): “[10] conjecture that in case of unbounded dividend intensity, horizontal barrier strategies are optimal for the maximization of the di erence of the expected discounted dividends and the de cit at ruin.”
Moments of the Dividend Payments and Related Problems in a Markov-Modulated Risk Model (2007, unknown): “Moreover, we have, for 0 u b and i E, u chV (u ch; b) V (u; b)i i ( )V (u ch; b) V (u ch x; b) dF (x)i i i i i i 0h m o(h) V (u ch; b) .”
De Finetti's optimal dividends problem with an affine penalty function at ruin (2010, background): “…and Gerber, Lin and Yang [17] looked at related value functions and problems in the compound Poisson setting; the case S = 0 and K = 1 was discussed in [15, 19] and a numerical study, for penalty functions taking the form of a polynomial of degree less than or equal to 2, was carried out in [17].”
The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model (2008, methodology): “E. Formula (5.4) can be obtained by reasoning as in Gerber et al. (2006): consider a particular sample path of the surplus process starting at u < b and in state i.”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “As a result, it can be argued probabilistically that Ex [ e−qτ + b ; τ+b < τd ] shall be the ratio of a function evaluated at x over the same function evaluated at b (see Gerber et al. 2006).”