Abstract
AbstractWe introduce a new class of singular stochastic control problems in which the process controller not only chooses the push intensity, at a price proportional to the displacement caused by his action, but he can also change the allowable control direction, paying a fixed cost for each such switching. Singular control of the one-dimensional Brownian motion with quadratic instantaneous cost function and costly direction switching on the infinite time horizon is analyzed in detail, leading to a closed-form solution. This example is used as an illustration of qualitative differences between the class of problems considered here and classic singular stochastic control.
Publisher
Springer Science and Business Media LLC
Subject
Management Science and Operations Research,General Mathematics,Software
Reference46 articles.
1. Abramowitz M, Stegun IA (eds) (1972) Solutions of quartic equations, §3.8.3 in Handbook of mathematical functions with formulas, graphs, and mathematical tables, 9th printing, Dover, New York, pp 17–18
2. Alvarez LHA (1999) A class of solvable stochastic control problems. Stoch Rep 67:83–122
3. Alvarez LHA (2000) Singular stochastic control, linear diffusions, and optimal stopping: a class of solvable problems. SIAM J Control Optim 39:1697–1710
4. Bather JA, Chernoff H (1967) Sequential decisions in the control of the spaceship. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability 3, University of California Press, Berkeley, CA, pp 181–207
5. Bather JA, Chernoff H (1967) Sequential decisions in the control of the spaceship (finite fuel). J Appl Probab 49:584–604