A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics

Baten Md. Azizul () and Khalid Ruzelan ()
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Baten Md. Azizul: Department of Statistics, School of Physical Sciences, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh
Khalid Ruzelan: Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia

Stochastics and Quality Control, 2020, vol. 35, issue 2, 43-55

Abstract: This study considers a stochastic control model in which an economic unit has productive capital and liabilities in the form of debt. The worth of capital changes over time through investment and random Brownian fluctuations in the unit price of capital. Income from production is also subject to the random Brownian fluctuations. The existence of the solutions to the associated Hamilton Jacobi Bellman equation for this model is established and the optimal policies are characterized. The optimal advertising rate as a function of the market share, the optimal consumption rate and the fraction of the wealth invested in stock at any time are obtained. The worth of the capital and the optimal consumption policy are derived for the stochastic optimal investment consumption model associated with the Hamilton Jacobi Bellman equation. Analysis and numerical simulations are then presented.

Keywords: Markov Process; Stochastic Differential Equation; Optimal Control and Diffusion Process (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/eqc-2020-0017

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