On the optimal dividend problem for a spectrally negative Lévy process

By Florin Avram, Zbigniew Palmowski, Martijn Pistorius. 2007

309 citations recorded by the source corpus.

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy 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 L\'{e}vy 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.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3d9a2ad5ed5e51a71172e260543a40bcdffa3ad4

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Citations in the corpus

De Finetti's optimal dividends problem with an affine penalty function at ruin (2010, background): “In the next section, we state some facts about scale functions and prove Theorem 1.2.”
General tax Structures and the Lévy Insurance Risk Model (2009, background): “1) constitute a subclass of controlled Lévy risk processes, the latter being of popular interest in recent literature; see, for example, [5], [13], and [14].”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, background): “[9] with global minimum at b∗ given by”
On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, background): “[3], Kyprianou and Palmowski [21], and Loeffen [27]) are two common examples.”
Optimal investment policy and dividend payment strategy in an insurance company (2010, background): “Azcue and Muler (2005) consider the problem of maximizing the cumulative expected discounted dividend pay-outs of an insurance company when the management has the possibility of controlling the risk exposure by reinsurance.”
Optimal dividends in the dual model under transaction costs (2013, unknown): “5 of [ 14] and Proposition 2 of [5] thatZ(c)/W (c) → q/Φ(q) ∈ (0,∞) andR(c)/W (c) → q/Φ(q)(2) ∈ (0,∞) asc ↑ ∞, respectively.”
Optimal dividends problem with a terminal value for spectrally positive Levy processes (2013, background): “Avram et al (2007), Loeffen (2008) and Kyprianou et al. (2010) studied the case of S = 0 for spectrally negative Lévy processes.”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “…in the theory of optimal stopping Avram et al. (2002, 2004); Alili and Kyprianou (2005) and Kyprianou (2006), in the theory of optimal control Avram et al. (2007) and Loeffen (2007), in the theory of queuing and storage models Dube et al. (2004) and Bekker et al. (2007), in the theory of…”
Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem (2008, methodology): “In much greater generality, the paper [2] focuses on the spectrally negative case and finds sufficient conditions for the optimal strategy to consist of a simple barrier strategy.”
An optimal dividends problem with transaction costs for spectrally negative Lévy processes (2009, unknown): “[4], Loeffen [20] showed that optimality of the barrier strategy for the de Finetti problem depends on the shape of the so-called scale function of a spectrally negative Lévy process.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “[10], by imposing some additional assumptions on the underlying Lévy process, X .”
Special, conjugate and complete scale functions for spectrally negative Lévy processes (2007, background): “For example, in the theory of optimal stopping [1; 2] and [38], in the theory of optimal control [3], [40; 51] and [44], in the theory of queuing and storage models [21] and [4], in the theory of branching processes [10], [29] and [43], in the theory of insurance risk and ruin [15], [34], [33], [20]”
An Optimal Dividends Problem with a Terminal Value for Spectrally Negative Lévy Processes with a Completely Monotone Jump Density (2009, background): “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”
On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes (2008, unknown): “We present our main results in Section 4 and prove them in Section 5 using some earlier results from Avram, Palmowski and Pistorius [3].”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “Spectrally negative Lévy processes have been considered recently in Avram et al. (2007), Biffis and Kyprianou (2010), Erder and Klüppelberg (2009), Kyprianou et al. (2010), Loeffen (2009), Renaud and Zhou (2007), among others, in the context of insurance risk models.”