Solving stochastic differential equations through genetic programming and automatic differentiation

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  author =       "Waldir Jesus {de Araujo Lobao} and 
                 Marco Aurelio Cavalcanti Pacheco and Douglas {Mota Dias} and 
                 Ana Carolina Alves Abreu",
  title =        "Solving stochastic differential equations through
                 genetic programming and automatic differentiation",
  journal =      "Engineering Applications of Artificial Intelligence",
  year =         "2018",
  volume =       "68",
  pages =        "110--120",
  month =        feb,
  keywords =     "genetic algorithms, genetic programming, Evolutionary
                 algorithm, Automatic differentiation, Stochastic
                 differential equations, Stochastic calculus, Geometric
                 Brownian motion",
  ISSN =         "0952-1976",
  URL =          "",
  DOI =          "doi:10.1016/j.engappai.2017.10.021",
  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