×

The corporate optimal portfolio and consumption choice problem in the real project with borrowing rate higher than deposit rate. (English) Zbl 1131.91350

Summary: One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond (bank account) and in a real project which has the production. The bank pays at an interest rate for any deposit and takes at a large rate for any loan. The optimal strategies are obtained by Hamilton-Jacobi-Bellman equation which is derived from dynamic programming principle. We also give the economic analysis to the optimal choice using the investment theory. For the specific hyperbolic absolute risk aversion case, we get the explicit optimal investment and consumption solution. At last, we give some simulation results to illustrate the optimal result and the influence of the volatility parameter on the optimal choice.

MSC:

91B28 Finance etc. (MSC2000)
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
93E03 Stochastic systems in control theory (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Merton, R., Continuous-Time Finance (1990), Blackwell Publishers: Blackwell Publishers Oxford
[2] Duffie, D., Dynamic Asset Pricing Theory (1992), Princeton University Press: Princeton University Press Princeton
[3] Karatzas, I., Optimization problems in the theory of continuous trading, SIAM J. Control Optim., 27, 5, 1221-1259 (1987) · Zbl 0701.90008
[4] Bellalah, M.; Wu, Z., Corporate international investment and diversification, Fin. India, 16, 3, 977-989 (2002)
[5] Karoui, N. El.; Peng, S.; Quenez, M. C., Backward stochastic differential equation in finance, Math. Fin., 7, 1-71 (1997) · Zbl 0884.90035
[6] Adler, M.; Dumas, B., Exposure to currency risk: definition and measurement, Fin. Manage., 3, 1, 41-50 (1984)
[7] Banks, H. T.; Crowley, J. M.; Kunisch, K., Cubic spline approximation techniques for parameter estimation in distributed systems, IEEE Trans. Auto. Control., AC-28, 773-786 (1983) · Zbl 0529.93021
[8] Yong, J. M.; Zhou, X. Y., Stochastic Controls: Hamiltonian Systems and HJB Equations (1999), Springer-Verlag: Springer-Verlag New York · Zbl 0943.93002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.