Optimal Control Strategies for Stochastic/Deterministic Bioeconomic Models
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.
KeywordsOptimal Control Problem Stochastic Differential Equation Singular Integral Equation Fractional Brownian Motion Hurst Parameter
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