Solving stochastic differential equations through genetic programming and automatic differentiation
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- @Article{deAraujo:2018:EAAI,
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author = "Waldir Jesus {de Araujo Lobao} and
Marco Aurelio Cavalcanti Pacheco and Douglas {Mota Dias} and
Ana Carolina Alves Abreu",
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title = "Solving stochastic differential equations through
genetic programming and automatic differentiation",
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journal = "Engineering Applications of Artificial Intelligence",
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year = "2018",
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volume = "68",
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pages = "110--120",
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month = feb,
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keywords = "genetic algorithms, genetic programming, Evolutionary
algorithm, Automatic differentiation, Stochastic
differential equations, Stochastic calculus, Geometric
Brownian motion",
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ISSN = "0952-1976",
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URL = "https://www.sciencedirect.com/science/article/pii/S0952197617302749",
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DOI = "doi:10.1016/j.engappai.2017.10.021",
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abstract = "This paper investigates the potential of evolutionary
algorithms, developed using a combination of genetic
programming and automatic differentiation, to obtain
symbolic solutions to stochastic differential
equations. Using the MATLAB programming environment and
based on the theory of stochastic calculus, we develop
algorithms and conceive a new methodology of
resolution. Relative to other methods, this method has
the advantages of producing solutions in symbolic form
and in continuous time and, in the case in which an
equation of interest is completely unknown, of offering
the option of algorithms that perform the specification
and estimation of the solution to the equation via a
real database. The last advantage is important because
it determines an appropriate solution to the problem
and simultaneously eliminates the difficult task of
arbitrarily defining the functional form of the
stochastic differential equation that represents the
dynamics of the phenomenon under analysis. The equation
for geometric Brownian motion, which is usually applied
to model prices and returns from financial assets, was
employed to illustrate and test the quality of the
algorithms that were developed. The results are
promising and indicate that the proposed methodology
can be a very effective alternative for resolving
stochastic differential equations.",
- }
Genetic Programming entries for
Waldir J A Lobao
Marco Aurelio Cavalcanti Pacheco
Douglas Mota Dias
Ana Carolina Alves Abreu
Citations