Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A continuous selection for optimal portfolios under convex risk measures
  does not always exist   One of the crucial problems in mathematical finance is to mitigate the risk
of a financial position by setting up hedging positions of eligible financial
securities. This leads to focusing on set-valued maps associating to any
financial position the set of those eligible payoffs that reduce the risk of
the position to a target acceptable level at the lowest possible cost. Among
other properties of such maps, the ability to ensure lower semicontinuity and
continuous selections is key from an operational perspective. It is known that
lower semicontinuity generally fails in an infinite-dimensional setting. In
this note we show that neither lower semicontinuity nor, more surprisingly, the
existence of continuous selections can be a priori guaranteed even in a
finite-dimensional setting. In particular, this failure is possible under
arbitrage-free markets and convex risk measures.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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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: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex