A variational problem arising in financial economics. (English) Zbl 0734.90009
Summary: We provide sufficient conditions for a dynamic consumption-portfolio problem in continuous time to have a solution. When the price processes satisfy a regularity condition, all utility functions that are continuous, increasing, concave, and are dominated by a strictly concave power function admit a solution.
References:
| [1] | Aumann, R.; Perles, M., A variational problem arising in economics, Journal of Mathematical Analysis and Applications, 11, 488-503 (1965) · Zbl 0137.39201 |
| [2] | Chung, K.; Williams, R., An introduction to stochastic integration (1983), Birkhauser Inc: Birkhauser Inc Boston, MA · Zbl 0527.60058 |
| [3] | Clark, J., The representation of functionals of Brownian motion by stochastic integrals, Annals of Mathematical Statistics, 41, 1282-1296 (1970) · Zbl 0213.19402 |
| [4] | Clark, J., Erratum, Annals of Mathematical Statistics, 42, 1778 (1971) |
| [5] | Cox, J.; Huang, C., A variational problem arising in financial economics with an application to a portfolio turnpike theorem, Working paper no. 1751-86 (1985), Sloan School of Management, Massachusetts Institute of Technology: Sloan School of Management, Massachusetts Institute of Technology Cambridge, MA |
| [6] | Cox, J.; Huang, C., Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory, 49, 33-83 (1989) · Zbl 0678.90011 |
| [7] | Dellacherie, C.; Meyer, P., Probabilities and potential B: Theory of martingales (1982), North-Holland: North-Holland New York · Zbl 0494.60002 |
| [8] | Dunford, N.; Schwartz, J., Linear operators, Part I: General theory (1957), Wiley: Wiley New York |
| [9] | Dybvig, P., A positive wealth constraint precludes arbitrage in the Black-Scholes model, manuscript (1980), Yale University: Yale University New Haven, CT, unpublished |
| [10] | Dybvig, P.; Huang, C., Nonnegative wealth, absence of arbitrage and feasible consumption plans, Review of Financial Studies, 1, 377-401 (1989) |
| [11] | Harrison, M.; Kreps, D., Martingales and multiperiod securities markets, Journal of Economic Theory, 20, 381-408 (1979) · Zbl 0431.90019 |
| [12] | Harrison, M.; Pliska, S., Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, 11, 215-260 (1981) · Zbl 0482.60097 |
| [13] | Holmes, R., Geometric functional analysis and its applications (1975), Springer-Verlag: Springer-Verlag New York · Zbl 0336.46001 |
| [14] | Huang, C., Information structure and viable price systems, Journal of Mathematical Economics, 14, 215-240 (1985) · Zbl 0606.90012 |
| [15] | Karatzas, I.; Lehoczky, J.; Shreve, S., Optimal portfolio and consumption decisions for a ‘small investor’ on afinite horizon, SIAM Journal of Control and Optimization, 25, 1557-1586 (1987) · Zbl 0644.93066 |
| [16] | Kreps, D., Arbitrage and equilibrium in economies with infinitely many commodities, Journal of Mathematical Economics, 8, 15-35 (1981) · Zbl 0454.90010 |
| [17] | Lipster, R.; Shiryayev, A., Statistics of random processes I: General theory (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0364.60004 |
| [18] | Merton, R., Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 1, 247-257 (1969) |
| [19] | Merton, R., Optimum consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3, 373-413 (1971) · Zbl 1011.91502 |
| [20] | Pliska, S., A stochastic calculus model of continuous trading: Optimal portfolios, Mathematics of Operations Research, 11, 371-382 (1986) · Zbl 1011.91503 |
| [21] | Rockafellar, R., Integral functionals, normal integrands and measurable selections, (Gossez, J., Nonlinear operators and the calculus of variations (1975), Springer-Verlag: Springer-Verlag New York) · Zbl 0374.49001 |
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.
