On Gerber-Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function

DOI10.1214/14-AAP1038zbMath1322.60055arXiv1110.4965MaRDI QIDQ2354887

Zbigniew Palmowski, Florin Avram, Martijn R. Pistorius

Publication date: 27 July 2015

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4965

zbMATH Keywords

Hamilton-Jacobi-Bellman equationdynamic programmingstochastic controlimpulse controlsingular controlstochastic solutionGerber-Shiu functionsstate-constraint problemLévy risk processoptimal dividend distributionde Finetti model

Mathematics Subject Classification ID

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Cites Work

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• An optimal dividends problem with transaction costs for spectrally negative Lévy processes
• A note on scale functions and the time value of ruin for Lévy insurance risk processes
• De Finetti's optimal dividends problem with an affine penalty function at ruin
• Optimal dividend strategies for a risk process under force of interest
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes
• Optimal dividend strategies in a Cramér-Lundberg model with capital injections
• Convexity and smoothness of scale functions and de Finetti's control problem
• Dividend maximization under consideration of the time value of ruin
• Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options
• Viscosity solutions of nonlinear integro-differential equations
• On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum
• Optimal dividend payout under compound Poisson income
• Optimal dividend policies for compound Poisson processes: the case of bounded dividend rates
• On the optimal dividend problem for a spectrally negative Lévy process
• A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation
• Introductory lectures on fluctuations of Lévy processes with applications.
• Stochastic Perron’s method and verification without smoothness using viscosity comparison: The linear case
• The Theory of Scale Functions for Spectrally Negative Lévy Processes
• Optimal Consumption for General Diffusions with Absorbing and Reflecting Barriers
• OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMER-LUNDBERG MODEL
• A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier
• Optimal Control with State-Space Constraint I
• Band strategies: The random walk of reserves
• Equqtions D'Hamilton-Jacobi Du Premier Ordre Avec Termes Intégro-Différentiels
• On degenerate elliptic-parabolic operators of second order and their associated diffusions
• Some Optimal Dividends Problems
• Optimal Dividend Strategies for a Compound Poisson Process Under Transaction Costs and Power Utility
• On the expectation of total discounted operating costs up to default and its applications
• Games of Economic Survival with Discrete- and Continuous-Income Processes
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
• Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach

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