×

An application of dynamic programming principle in corporate international optimal investment and consumption choice problem. (English) Zbl 1205.91150

Summary: This paper is concerned with a kind of corporate international optimal portfolio and consumption choice problems, in which the investor can invest her or his wealth either in a domestic bond (bank account) or in an oversea real project with production. The bank pays a lower interest rate for deposit and takes a higher rate for any loan. First, we show that Bellman’s dynamic programming principle still holds in our setting; second, in terms of the foregoing principle, we obtain the investor’s optimal portfolio proportion for a general maximizing expected utility problem and give the corresponding economic analysis; third, for the special but nontrivial Constant Relative Risk Aversion (CRRA) case, we get the investors optimal investment and consumption solution; last but not least, we give some numerical simulation results to illustrate the influence of volatility parameters on the optimal investment strategy.

MSC:

91G10 Portfolio theory
49L20 Dynamic programming in optimal control and differential games
91B16 Utility theory
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] J. J. Choi, “Diversification, exchange risk, and corporate international investment,” Journal of International Business Studies, pp. 145-155, 1989.
[2] D. Duffie, Dynamic Asset Picing Theory, Princeton University Press, Princeton, NJ, USA, 1992.
[3] R. Merton, Continuous-Time Finance, Blackwell, Oxford, Uk, 1991. · Zbl 1019.91502
[4] T. Zariphopoulou, “Investment-consumption models with transaction fees and Markov-chain parameters,” SIAM Journal on Control and Optimization, vol. 30, no. 3, pp. 613-636, 1992. · Zbl 0784.90027 · doi:10.1137/0330035
[5] T. Zariphopoulou, “Consumption-investment models with constraints,” SIAM Journal on Control and Optimization, vol. 32, no. 1, pp. 59-85, 1994. · Zbl 0790.90007 · doi:10.1137/S0363012991218827
[6] M. Bellalah and Z. Wu, “A simple model of corporate international investment under incomplete information and taxes,” Annals of Operations Research, vol. 165, no. 1, pp. 123-143, 2009. · Zbl 1163.91379 · doi:10.1007/s10479-007-0307-9
[7] G. C. Wang and Z. Wu, “General maximum principles for partially observed risk-sensitive optimal control problems and applications to finance,” Journal of Optimization Theory and Applications, vol. 141, no. 3, pp. 677-700, 2009. · Zbl 1178.49049 · doi:10.1007/s10957-008-9484-1
[8] N. El Karoui, S. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1-71, 1997. · Zbl 0884.90035 · doi:10.1111/1467-9965.00022
[9] R. Bellman, “On the theory of dynamic programming,” Proceedings of the National Academy of Sciences of the United States of America, vol. 38, pp. 716-719, 1952. · Zbl 0047.13802 · doi:10.1073/pnas.38.8.716
[10] J. Mukuddem-Petersen and M. A. Petersen, “Bank management via stochastic optimal control,” Automatica, vol. 42, no. 8, pp. 1395-1406, 2006. · Zbl 1108.93079 · doi:10.1016/j.automatica.2006.03.012
[11] J. Mukuddem-Petersen and M. A. Petersen, “Optimizing asset and capital adequacy management in banking,” Journal of Optimization Theory and Applications, vol. 137, no. 1, pp. 205-230, 2008. · Zbl 1141.91020 · doi:10.1007/s10957-007-9322-x
[12] I. Karatzas, “Optimization problems in the theory of continuous trading,” SIAM Journal on Control and Optimization, vol. 27, no. 6, pp. 1221-1259, 1987. · Zbl 0701.90008 · doi:10.1137/0327063
[13] R. Bellman, Dynamic Programming, Princeton University Press, Princeton, NJ, USA, 1957. · Zbl 0077.13605
[14] S. G. Peng, “A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation,” Stochastics and Stochastics Reports, vol. 38, no. 2, pp. 119-134, 1992. · Zbl 0756.49015
[15] N. El Karoui and M.-C. Quenez, “Dynamic programming and pricing of contingent claims in an incomplete market,” SIAM Journal on Control and Optimization, vol. 33, no. 1, pp. 29-66, 1995. · Zbl 0831.90010 · doi:10.1137/S0363012992232579
[16] J. Yong and X. Y. Zhou, Stochastic Control: Hamiltonian Systems and HJB Equations, vol. 43 of Applications of Mathematics, Springer, New York, NY, USA, 1999. · Zbl 0943.93002
[17] T. Bosch, J. Mukuddem-Petersen, M. A. Petersen, and I. Schoeman, “Optimal auditing in the banking industry,” Optimal Control Applications & Methods, vol. 29, no. 2, pp. 127-158, 2008. · doi:10.1002/oca.828
[18] M. A. Petersen, M. C. Senosi, and J. Mukuddem-Petersen, Subprime Mortgage Models, Nova, New York, NY, USA, 2010. · Zbl 1230.91184
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.