Stochastic Optimal Control and Simulations with Application to the Cashew Nut Sector in Senegal
Amadou Saikou Diallo  1@  , Steeven Belvinos Affognon  2@  , Babacar Mbaye Ndiaye  3@  , Philip Ngare  2@  
1 : Laboratory of mathematics and applications. University of Assane SECK, Ziguinchor. BP 523, Senegal.
2 : School of Mathematics, University of Nairobi. P.O. Box 30197-00100, Nairobi, Kenya.
3 : Laboratory of Mathematics of Decision and Numerical Analysis. Cheikh Anta Diop University. BP 45087 Dakar-Fann, Senegal.

In this article, we propose a new methodology based on stochastic optimal control problems, to solve the revenue and exploitation issues of the cashew nut sector in Senegal (West Africa). First, we reviewed some underlying tools from stochastic calculus such as stochastic processes, Brownian motion, martingales, and stochastic differential equations. The stochastic optimal sales plan and agricultural exploitation plan are determined using the Hamiltonian-Bellman-Jacobi equations that correspond to the proposed maximization problems in this paper. Finally, numerical simulations and real data from Casamance (Southern Senegal) were used to analyze the performance of this novel approach to the cashew nut sector.

 


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