A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
-
Md. Azizul Baten
und
Ruzelan Khalid
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.
References
[1] S. Attaway, Matlab: A Practical Introduction to Programming and Problem Solving, Elsevier, Oxford, 2013. 10.1016/B978-0-12-405876-7.00003-1Suche in Google Scholar
[2] R. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957. Suche in Google Scholar
[3] T. R. Bielecki and S. R. Pliska, Risk-sensitive dynamic asset management, Appl. Math. Optim. 39 (1999), no. 3, 337–360. 10.1007/s002459900110Suche in Google Scholar
[4] N. A. Derzko and S. P. Sethi, Optimal exploration and consumption of a natural resource—Stochastic case, Internat. J. Policy Anal. Inform. Systems 5 (1981), no. 3, 185–200. Suche in Google Scholar
[5] E. J. Dockner and G. Feichtingor, Cyclical consumption patterns and rational addiction, Amer. Econom. Rev. 83 (1993), 256–263. Suche in Google Scholar
[6] W. H. Fleming and T. Pang, An application of stochastic control theory to financial economics, SIAM J. Control Optim. 43 (2004), no. 2, 502–531. 10.1137/S0363012902419060Suche in Google Scholar
[7] W. H. Fleming and T. Pang, A stochastic control model of investment, production and consumption, Quart. Appl. Math. 63 (2005), no. 1, 71–87. 10.1090/S0033-569X-04-00941-1Suche in Google Scholar
[8] W. H. Fleming and S. J. Sheu, Risk-sensitive control and an optimal investment model, Math. Finance 10 (2000), no. 2, 197–213. 10.1111/1467-9965.00089Suche in Google Scholar
[9] B. Hahn and D. Valentine, Essential MATLAB for Engineers and Scientists, Elsevier, Oxford, 2013. 10.1016/B978-0-12-394398-9.00028-9Suche in Google Scholar
[10] D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev. 43 (2001), no. 3, 525–546. 10.1137/S0036144500378302Suche in Google Scholar
[11] X. Mao, Stochastic Differential Equations and Applications, Woodhead Publishing Limited, Cambridge, 2011. 10.1533/9780857099402.47Suche in Google Scholar
[12] R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Rev. Econom. Stat. 51 (1969), no. 3, 247–257. 10.2307/1926560Suche in Google Scholar
[13] A. Novak and G. Feichtinger, Optimal consumption, training, working time, and leisure over the life cycle, J. Optim. Theory Appl. 75 (1992), no. 2, 369–388. 10.1007/BF00941474Suche in Google Scholar
[14] T. Pang, Stochastic Control Theory and Its Applications to Financial Economics, Brown University, Providence, 2002. Suche in Google Scholar
[15] T. Pang, Portfolio optimization models on infinite-time horizon, J. Optim. Theory Appl. 122 (2004), no. 3, 573–597. 10.1023/B:JOTA.0000042596.26927.2dSuche in Google Scholar
[16] S. P. Sethi, Optimal Consumption an Investment with Bankruptcy, Kluwer Academic Publishers, Boston, 1997. 10.1007/978-1-4615-6257-3Suche in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
- Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method
- The Reflected-Shifted-Truncated Lindley Distribution with Applications
- The Marshall–Olkin Transmuted-G Family of Distributions
- Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times
Artikel in diesem Heft
- Frontmatter
- A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
- Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method
- The Reflected-Shifted-Truncated Lindley Distribution with Applications
- The Marshall–Olkin Transmuted-G Family of Distributions
- Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times
