Optimal Control Strategies for Stochastic/Deterministic Bioeconomic Models

  • Darya Filatova
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


In this work the new model, namely the stochastic differential equation with multifractional Brownian motion, is proposed to describe the dynamics of the population in the task of the optimal fishery management. To avoid the problems of the identifiability of the model and to take into account the discounted rate of the population, the stochastic control problem is transformed to the deterministic one by suitable moments approximation of the order 0 < γ < 1. This transformation results the singular integral equation as the control object equation. Taking into account both control and state constraints and applying the variation calculus we derive the first-order necessary conditions in the form of the local maximum principle.


Optimal Control Problem Stochastic Differential Equation Singular Integral Equation Fractional Brownian Motion Hurst Parameter 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Dorodnicyn Computing Centre of RASMoscowRussian Federation UJK, Kielce, Poland
  2. 2.UJKKielcePoland

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