Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An SMP-Based Algorithm for Solving the Constrained Utility Maximization
  Problem via Deep Learning   We consider the utility maximization problem under convex constraints with
regard to theoretical results which allow the formulation of algorithmic
solvers which make use of deep learning techniques. In particular for the case
of random coefficients, we prove a stochastic maximum principle (SMP), which
also holds for utility functions $U$ with $\mathrm{id}_{\mathbb{R}^{+}} \cdot
U'$ being not necessarily nonincreasing, like the power utility functions,
thereby generalizing the SMP proved by Li and Zheng (2018). We use this SMP
together with the strong duality property for defining a new algorithm, which
we call deep primal SMP algorithm. Numerical examples illustrate the
effectiveness of the proposed algorithm - in particular for higher-dimensional
problems and problems with random coefficients, which are either path dependent
or satisfy their own SDEs. Moreover, our numerical experiments for constrained
problems show that the novel deep primal SMP algorithm overcomes the deep SMP
algorithm's (see Davey and Zheng (2021)) weakness of erroneously producing the
value of the corresponding unconstrained problem. Furthermore, in contrast to
the deep controlled 2BSDE algorithm from Davey and Zheng (2021), this algorithm
is also applicable to problems with path dependent coefficients. As the deep
primal SMP algorithm even yields the most accurate results in many of our
studied problems, we can highly recommend its usage. Moreover, we propose a
learning procedure based on epochs which improved the results of our algorithm
even further. Implementing a semi-recurrent network architecture for the
control process turned out to be also a valuable advancement.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio