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SUMMARY:An SMP-Based Algorithm for Solving the Constrained Utility Maximiz
ation Problem via Deep Learning
DTSTART;VALUE=DATE-TIME:20220803T113000Z
DTEND;VALUE=DATE-TIME:20220803T115000Z
DTSTAMP;VALUE=DATE-TIME:20240815T051433Z
UID:indico-contribution-1199@conference2.aau.at
DESCRIPTION:We consider the utility maximization problem under convex cons
traints with regard to theoretical results which allow the formulation of
algorithmic solvers which make use of deep learning techniques. In particu
lar for the case of random coefficients\, we prove a stochastic maximum pr
inciple (SMP) generalizing the SMP proved by Li and Zheng (2018). We use t
his SMP together with the strong duality property for defining a new algor
ithm\, which we call deep primal SMP algorithm. Numerical examples illustr
ate the effectiveness of the proposed algorithm. Moreover\, our numerical
experiments for constrained problems show that the novel deep primal SMP a
lgorithm overcomes the deep SMP algorithm's (see Davey and Zheng (2021)) w
eakness of erroneously producing the value of the corresponding unconstrai
ned problem. Furthermore\, in contrast to the deep controlled 2BSDE algori
thm from Davey and Zheng (2021)\, this algorithm is also applicable to pro
blems with path dependent coefficients. Finally\, we propose a learning pr
ocedure based on epochs\, which improved the results of our algorithm even
further. Implementing a semi-recurrent network architecture for the contr
ol process turned out to be also a valuable advancement.\n\nhttps://confer
ence2.aau.at/event/131/contributions/1199/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1199/
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