OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMÉR‐LUNDBERG MODEL

By Pablo Azcue, Nora Muler. 2005

263 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/1c8668c74adee94e355e2478e0a4d683bede8e60

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Citations in the corpus

Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs (2014, methodology): “If v is twice continuously differentiable, then applying standard arguments from stochastic control theory (see Fleming and Soner [17]) or an approach similar to that in Azcue and Muler [9], we can show that”
Maximizing Dividends without Bankruptcy (2006, background): “1 If the initial surplus is greater than b*, the optimal strategy may be much more complicated; the reader may want to consult the book by Schmidli (2007) and also Azcue and Muler (2005).”
Optimal investment policy and dividend payment strategy in an insurance company (2010, methodology): “2 of Azcue and Muler (2005), we can show that for any λ ≥ λ0 = max{2m/δ,4m/M} the point (xλ, yλ) / ∈ ∂A. Using Theorem 3.2 of Crandall, Ishii and Lions (1992), it can be proved that for any δ > 0, there exist real numbers Aδ and Bδ such that”
Optimal Dividends in the Dual Model with Diffusion (2008, unknown): “In this model, the optimal dividend strategy is not a barrier strategy in general, and finding it is a challenge; see, for example, Bühlmann (1970), Azcue and Muler (2005) and Schmidli (2008).”
Optimal dividend strategies for a risk process under force of interest (2008, methodology): “The proofs are in the spirit of Azcue and Muler in [3].”
Dividend maximization under consideration of the time value of ruin (2007, methodology): “Recently, the optimal dividend problem in the compound Poisson model was taken up again by Azcue and Muler [2], who used stochastic optimal control techniques and viscosity solutions.”
On the optimal dividend problem for a spectrally negative Lévy process (2007, methodology): “Azcue and Muler [1] also constructed an example with c∗ = 0 and (Γvc∗ − qvc∗)(x) > 0 for some x > 0 where the optimal strategy does not take the form of a barrier strategy.”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, methodology): “Consider next the example in Azcue and Muller [7], with pure Erlang claims of order n = 2, with μ = 1, λ = 10, p = 1075 , q = 110 , θ = 7100 and Laplace exponent ψ(s) − q = ps + λ( μμ+s )2 − λ − q = p(μ+s)2 (s + ζ1)(s + ζ2)(s − ζ0), with ζ0 ≈ 0.0396, ζ1 ≈ 0.0794, ζ2 ≈ 1.4882.”
Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem (2008, unknown): “This result has been re-considered very recently in [3] for Cramér-Lundberg processes with a general jump distribution.”
A Risk Model with Multilayer Dividend Strategy (2007, background): “One should keep in mind, however, that this optimality property does not carry over to arbitrary claim size distributions (see, e.g., Azcue and Muler 2005; Albrecher and Thonhauser 2006; Schmidli 2007).”
Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process (2007, background): “Plugging the above back into (4) we now see the iteration”
Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle (2012, methodology): “4) For any 0 < ρ < 1, define a new control policy π = (a, L) for initial surplus ρx1 + (1− ρ)x2 such that at = ρa (1) t + (1− ρ)a (2) t , Lt = ρL (1) t + (1− ρ)L (2) t .”
ON OPTIMAL DIVIDENDS IN THE DUAL MODEL (2012, methodology): “Regarding the spectrally negative Lévy model, we refer the reader to [6] for examples where barrier strategies are suboptimal and to [15] for a sufficient condition for optimality.”
Optimal dividends problem with a terminal value for spectrally positive Levy processes (2013, background): “Moreover, Azcue and Muler (2005) have provided a counter-example for the case S = 0 shows that a barrier strategy can not be optimal.”
An Optimal Dividends Problem with a Terminal Value for Spectrally Negative Lévy Processes with a Completely Monotone Jump Density (2009, unknown): “When S = 0 the above optimal control problem transforms, albeit within the more general framework of a spectrally negative Lévy risk process, to the original optimal dividends problem introduced firstly in a discrete time setting by de Finetti [7] and later studied in, amongst others, [3, 4, 12, 19,”
De Finetti's optimal dividends problem with an affine penalty function at ruin (2010, result): “This is in contrast with the dividend problem with capital injections considered in [7, 21]: there a barrier strategy always forms the optimal strategy, no matter the form of the jump measure.”
An optimal dividends problem with transaction costs for spectrally negative Lévy processes (2009, unknown): “This example corresponds to the one in Azcue and Muler [5] for which they showed that the optimal strategy for the de Finetti problem is not a barrier strategy.”