Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimal Dividend Problem with Capital Injections over a Finite
  Horizon   In this paper we propose and solve an optimal dividend problem with capital
injections over a finite time horizon. The surplus dynamics obeys a linearly
controlled drifted Brownian motion that is reflected at the origin, dividends
give rise to time-dependent instantaneous marginal profits, whereas capital
injections are subject to time-dependent instantaneous marginal costs. The aim
is to maximize the sum of a liquidation value at terminal time and of the total
expected profits from dividends, net of the total expected costs for capital
injections. Inspired by the study of El Karoui and Karatzas (1989) on reflected
follower problems, we relate the optimal dividend problem with capital
injections to an optimal stopping problem for a drifted Brownian motion that is
absorbed at the origin. We show that whenever the optimal stopping rule is
triggered by a time-dependent boundary, the value function of the optimal
stopping problem gives the derivative of the value function of the optimal
dividend problem. Moreover, the optimal dividend strategy is also triggered by
the moving boundary of the associated stopping problem. The properties of this
boundary are then investigated in a case study in which instantaneous marginal
profits and costs from dividends and capital injections are constants
discounted at a constant rate.

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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: chem-ph