Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Gerber-Shiu functions and optimal dividend distribution for a
  L\'{e}vy risk process in the presence of a penalty function   This paper concerns an optimal dividend distribution problem for an insurance
company whose risk process evolves as a spectrally negative L\'{e}vy process
(in the absence of dividend payments). The management of the company is assumed
to control timing and size of dividend payments. The objective is to maximize
the sum of the expected cumulative discounted dividend payments received until
the moment of ruin and a penalty payment at the moment of ruin, which is an
increasing function of the size of the shortfall at ruin; in addition, there
may be a fixed cost for taking out dividends. A complete solution is presented
to the corresponding stochastic control problem. It is established that the
value-function is the unique stochastic solution and the pointwise smallest
stochastic supersolution of the associated HJB equation. Furthermore, a
necessary and sufficient condition is identified for optimality of a single
dividend-band strategy, in terms of a particular Gerber-Shiu function. A number
of concrete examples are analyzed.

25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas