On the Optimal Dividend Problem for a Spectrally Negative Lévy Process

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Lévy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes t...

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Bibliographische Detailangaben
Veröffentlicht in:	The Annals of Applied Probability. - Institute of Mathematical Statistics. - 17(2007), 1, Seite 156-180
1. Verfasser:	Avram, Florin (VerfasserIn)
Weitere Verfasser:	Palmowski, Zbigniew, Pistorius, Martijn R.
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2007
Zugriff auf das übergeordnete Werk:	The Annals of Applied Probability
Schlagworte:	Lévy process Dividend problem Local time Reflection Scale function Fluctuation theory Economics Mathematics Business Physical sciences Law


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100	1		\|a Avram, Florin \|e verfasserin \|4 aut
245	1	0	\|a On the Optimal Dividend Problem for a Spectrally Negative Lévy Process
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520			\|a In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Lévy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected discounted dividends. Related is the problem where we impose the restriction that ruin be prevented: the beneficiaries of the dividends must then keep the insurance company solvent by bail-out loans. Drawing on the fluctuation theory of spectrally negative Lévy processes we give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function, for either of the problems. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.
540			\|a Copyright 2007 Institute of Mathematical Statistics
650		4	\|a Lévy process
650		4	\|a Dividend problem
650		4	\|a Local time
650		4	\|a Reflection
650		4	\|a Scale function
650		4	\|a Fluctuation theory
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial investments \|x Investment returns \|x Dividends
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Business \|x Industry \|x Industrial sectors \|x Service industries \|x Insurance industry \|x Insurance providers \|x Insurance companies
650		4	\|a Physical sciences \|x Physics \|x Thermodynamics \|x Thermodynamic properties \|x Entropy \|x Fluctuation theorem
650		4	\|a Mathematics \|x Applied mathematics \|x Game theory \|x Strategic behavior \|x Optimal strategies
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Brownian motion
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions \|x Mathematical transformations \|x Integral transformations \|x Laplace transformation
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical inequalities \|x Variational inequalities
650		4	\|a Law \|x Civil law \|x Probate law \|x Property inheritance \|x Beneficiaries
650		4	\|a Economics \|x Economic disciplines \|x Financial economics \|x Finance \|x Financial investments \|x Investment returns \|x Dividends
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Business \|x Industry \|x Industrial sectors \|x Service industries \|x Insurance industry \|x Insurance providers \|x Insurance companies
650		4	\|a Physical sciences \|x Physics \|x Thermodynamics \|x Thermodynamic properties \|x Entropy \|x Fluctuation theorem
650		4	\|a Mathematics \|x Applied mathematics \|x Game theory \|x Strategic behavior \|x Optimal strategies
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Brownian motion
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions \|x Mathematical transformations \|x Integral transformations \|x Laplace transformation
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical inequalities \|x Variational inequalities
650		4	\|a Law \|x Civil law \|x Probate law \|x Property inheritance \|x Beneficiaries
655		4	\|a research-article
700	1		\|a Palmowski, Zbigniew \|e verfasserin \|4 aut
700	1		\|a Pistorius, Martijn R. \|e verfasserin \|4 aut
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