Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A zero-sum game between a singular stochastic controller and a
  discretionary stopper   We consider a stochastic differential equation that is controlled by means of
an additive finite-variation process. A singular stochastic controller, who is
a minimizer, determines this finite-variation process, while a discretionary
stopper, who is a maximizer, chooses a stopping time at which the game
terminates. We consider two closely related games that are differentiated by
whether the controller or the stopper has a first-move advantage. The games'
performance indices involve a running payoff as well as a terminal payoff and
penalize control effort expenditure. We derive a set of variational
inequalities that can fully characterize the games' value functions as well as
yield Markovian optimal strategies. In particular, we derive the explicit
solutions to two special cases and we show that, in general, the games' value
functions fail to be $C^1$. The nonuniqueness of the optimal strategy is an
interesting feature of the game in which the controller has the first-move
advantage.

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The categories of this paper are: funct-an
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol