Abstract
This work is dedicated to modelling economic dynamics with random time scale. We propose a solution in the form a continuous time model where interactions of agents are random exchanges of finite portions of products and money at random points in time. In this framework, the economic agent determines the volume, but not the moments of the transactions and their order. The paper presents a correct formal description of optimal consumption and borrowing as a stochastic optimal control problem, which we study using the optimality conditions in the Lagrange’s form. The solution appears to have a boundary layer near the end of planning horizon where the optimal control satisfies the specific functional equation. This equation was studied numerically using the functional Newton method adapted to a two-dimensional case.
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Acknowledgments.
The authors are very grateful to S. I. Bezrodnykh for valuable comments. This research was supported by the grant RFBR project 17-01-00588 A “Dynamic economic models with random time scale”.
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Zhukova, A., Pospelov, I. (2020). Numerical Analysis of the Model of Optimal Consumption and Borrowing with Random Time Scale. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_19
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