Consumption-investment problem with subsistence consumption, bankruptcy, and random market coefficients. (English) Zbl 0903.90019
Summary: We consider a general continuous-time finite-horizon single-agent consumption and portfolio decision problem with subsistence consumption and value of bankruptcy. Our analysis allows for random market coefficients and general continuously differentiable concave utility functions. We study the time of bankruptcy as a problem of optimal stopping, and succeed in obtaining explicit formulas for the optimal consumption and wealth processes in terms of the optimal bankruptcy time. This paper extends the results of I. Karatzas, J. P. Lehoczky and S. E. Shreve [SIAM J. Control Optimization 25, 1557-1586 (1987; Zbl 0644.93066)] on the maximization of expected utility from consumption in a financial market with random coefficients by incorporating subsistence consumption and bankruptcy. It also addresses the random coefficients and finite-horizon version of the problem treated by S. P. Sethi, M. I. Taksar and E. L. Presman [J. Econ. Dyn. Control 16, No. 3/4, 747-768 (1992; Zbl 0762.90005)]. The mathematical tools used in our analysis are optimal stopping, stochastic control, martingale theory, and Girsanov change of measure.
MSC:
| 91B62 | Economic growth models |
| 91B42 | Consumer behavior, demand theory |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 93E20 | Optimal stochastic control |
Keywords:
continuous-time finite-horizon single-agent consumption and portfolio decision problem; bankruptcy; optimal stopping; martingale theory; Girsanov change of measureReferences:
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