Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality for optimal consumption under no unbounded profit with bounded
  risk   We give a definitive treatment of duality for optimal consumption over the
infinite horizon, in a semimartingale incomplete market satisfying no unbounded
profit with bounded risk (NUPBR). Rather than base the dual domain on (local)
martingale deflators, we use a class of supermartingale deflators such that
deflated wealth plus cumulative deflated consumption is a supermartingale for
all admissible consumption plans. This yields a strong duality, because the
enlarged dual domain of processes dominated by deflators is naturally closed,
without invoking its closure. In this way we automatically reach the bipolar of
the set of deflators. We complete this picture by proving that the set of
processes dominated by local martingale deflators is dense in our dual domain,
confirming that we have identified the natural dual space. In addition to the
optimal consumption and deflator, we characterise the optimal wealth process.
At the optimum, deflated wealth is a supermartingale and a potential, while
deflated wealth plus cumulative deflated consumption is a uniformly integrable
martingale. This is the natural generalisation of the corresponding feature in
the terminal wealth problem, where deflated wealth at the optimum is a
uniformly integrable martingale. We use no constructions involving equivalent
local martingale measures. This is natural, given that such measures typically
do not exist over the infinite horizon and that we are working under NUPBR,
which does not require their existence. The structure of the duality proof
reveals an interesting feature compared with the terminal wealth problem.
There, the dual domain is $L^{1}$-bounded, but here the primal domain has this
property, and hence many steps in the duality proof show a marked reversal of
roles for the primal and dual domains, compared with the proofs of Kramkov and
Schachermayer.

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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph