Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proving Regularity of the Minimal Probability of Ruin via a Game of
  Stopping and Control   We reveal an interesting convex duality relationship between two problems:
(a) minimizing the probability of lifetime ruin when the rate of consumption is
stochastic and when the individual can invest in a Black-Scholes financial
market; (b) a controller-and-stopper problem, in which the controller controls
the drift and volatility of a process in order to maximize a running reward
based on that process, and the stopper chooses the time to stop the running
reward and rewards the controller a final amount at that time. Our primary goal
is to show that the minimal probability of ruin, whose stochastic
representation does not have a classical form as does the utility maximization
problem (i.e., the objective's dependence on the initial values of the state
variables is implicit), is the unique classical solution of its
Hamilton-Jacobi-Bellman (HJB) equation, which is a non-linear boundary-value
problem. We establish our goal by exploiting the convex duality relationship
between (a) and (b).

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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg