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

A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics AbstractThis 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

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

Economic Quality Control , Volume 35 (2): 13 – Dec 1, 2020

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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6147
eISSN
2367-2404
DOI
10.1515/eqc-2020-0017
Publisher site
See Article on Publisher Site

Abstract

AbstractThis 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.

Journal

Economic Quality Controlde Gruyter

Published: Dec 1, 2020

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