Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Brownian Models of Performance and Control
  • Cited by 59
Publisher:
Cambridge University Press
Online publication date:
December 2013
Print publication year:
2013
Online ISBN:
9781139087698
DOI:
https://doi.org/10.1017/CBO9781139087698
Subjects:
Economics, Finance and Accountancy, Applied Probability and Stochastic Networks, Statistics and Probability
Information

Book description

Direct and to the point, this book from one of the field's leaders covers Brownian motion and stochastic calculus at the graduate level, and illustrates the use of that theory in various application domains, emphasizing business and economics. The mathematical development is narrowly focused and briskly paced, with many concrete calculations and a minimum of abstract notation. The applications discussed include: the role of reflected Brownian motion as a storage model, queuing model, or inventory model; optimal stopping problems for Brownian motion, including the influential McDonald–Siegel investment model; optimal control of Brownian motion via barrier policies, including optimal control of Brownian storage systems; and Brownian models of dynamic inference, also called Brownian learning models or Brownian filtering models.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
Bartie, Robert G. 1976. The Elements of Real Analysis. Second edn. John Wiley & Sons, New York-London-Sydney. (Cited on pages xi, 179, 180, and 181.)
Bather, John, and Chernoff, Herman. 1967. Sequential Decisions in the Control of a Space-Ship (Finite Fuel). J. Appl. Probab., 4(3), 584–604. (Cited on page 135.)
Beneš, V. E., Shepp, L. A., and Witsenhausen, H. S. 1980. Some solvable stochastic control problems. Stochastics, 4, 39–83. (Cited on page 135.)
Bensoussan, A., and Lions, J. L. 1975. Nouvelles Methodes en Contrôle Impulsionnel. Applied Mathematics and Optimization, 1, 289–312. (Cited on page 134.)
Billingsley, Patrick. 1995. Probability and Measure. Third edn. Wiley Series in Probability and Mathematical Statistics. New York: Wiley-Interscience. (Cited on pages xi, 5, 177, and 179.)
Billingsley, Patrick. 1999. Convergence of Probability Measures. Second edn. Wiley Series in Probability and Statistics. New York: Wiley-Interscience. (Cited on pages 2 and 175.)
Breiman, Leo. 1968. Probability. Reading, MA: Addison-Wesley Publishing Company. (Cited on page 2.)
Chernoff, Herman. 1968. Optimal stochastic control. Sankhya A, 30(3), 221–252. (Cited on page 148.)
Chung, Kai Lai, and Williams, Ruth J. 1990. Introduction to Stochastic Integration. Second edn. Probability and its Applications. Boston: Birkhaauser. (Cited on pages 4, 7, 8, 67, and 177.)
Çinlar, Erhan. 1975. Introduction to Stochastic Processes. Englewood Cliffs, NJ: Prentice-Hall Inc. (Cited on pages 96 and 97.)
Curtiss, J. H. 1942. A note on the theory of moment generating functions. Ann. Math. Statist., 13(4), 430–433. (Cited on page 7.)
Daley, Brendan, and Green, Brett. 2012. Waiting for news in the market for lemons. Econometrica, 80(4), 1433–1504. (Cited on page 161.)
Dayanik, Savaş, and Karatzas, Ioannis. 2003. On the optimal stopping problem for one-dimensional diffusions. Stoch. Proc. Appl., 107, 173–212. (Cited on pages 85, 86, 88, and 134.)
DeGroot, Morris H. 2004. Optimal Statistical Decisions. Wiley Classics Library. Hobo-ken, NJ: Wiley-Interscience. (Cited on page 148.)
Dixit, Avinash. 1993. The Art ofSmooth Pasting. Chur, Switzerland: Harwood Academic Publishers. (Cited on page x.)
Dixit, Avinash K., and Pindyck, Robert S. 1994. Investment Under Uncertainty. Princeton, NJ: Princeton University Press. (Cited on page 88.)
Egami, Masahiko. 2008. A direct solution method for stochastic impulse control problems of one-dimensional diffusions. SIAM J. Control. Optimizat., 47(3), 1191–1218. (Cited on page 134.)
El Karoui, N., and Chaleyat-Maurel, M. 1978. Un problème de réflexion et ses aplica-tions au temps local et aux équations differentielles stochastiques sur ℝ-Cas continu. Astérisque, 52–53, 117–144. (Cited on page 20.)
Emanuel, David C., Harrison, J. Michael, and Taylor, Allison J. 1975. A diffusion approximation for the ruin function of a risk process with compounding assets. Scand. Actuar. J., 1975(4), 240–247. (Cited on pages 157 and 158.)
Harrison, J. Michael. 1973. Assembly-like queues. J. Appl. Probab., 10, 354–367. (Cited on page 34.)
Harrison, J. Michael. 1977. Ruin problems with compounding assets. Stoch. Proc. Appl., 5(1), 67–79. (Cited on page 158.)
Harrison, J. Michael. 1978. The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab, 10, 886–905. (Cited on page 32.)
Harrison, J. Michael, and Lemoine, Austin J. 1981. Sticky Brownian motion as the limit of storage processes. J. Appl. Probab., 18(1), 216–226. (Cited on page 165.)
Harrison, J. Michael, and Reiman, Martin I. 1981. Reflected Brownian motion on an orthant. Ann. Probab., 9(2), 302–308. (Cited on page 108.)
Harrison, J. Michael, and Taksar, Michael I. 1983. Instantaneous control of Brownian motion. Math. Oper. Res., 8(3), 439–453. (Cited on pages 110 and 134.)
Harrison, J. Michael, and Taylor, Allison J. 1978. Optimal control of a Brownian storage system. Stoch. Proc. Appl., 6(2), 179–194. (Cited on page 134.)
Harrison, J. Michael, Sellke, Thomas M., and Taylor, Allison J. 1983. Impulse control of Brownian motion. Math. Oper. Res., 8(3), 454–466. (Cited on page 134.)
Karatzas, Ioannis, and Shreve, Steven E. 1991. Methods of Mathematical Finance. New York: Springer. (Cited on page 88.)
Karatzas, Ioannis, and Shreve, Steven E. 1998. Brownian Motion and Stochastic Calculus. 2nd edn. New York: Springer. (Cited on pages 12, 52, 60, and 177.)
Kruk, Lukasz, Lehoczky, John, Ramanan, Kavita, and Shreve, Steven. 2007. An explicit formula for the Skorokhod map on [0, a]. Ann. Probab., 35(5), 1740–1768. (Cited on page 22.)
Liptser, Robert S., and Shiryayev, Albert N. 2000a. Statistics of Random Processes I. 2nd rev. and exp. edn. Springer. Translated by A. B. Aries. (Cited on page 150.)
Liptser, Robert S., and Shiryayev, Albert N. 2000b. Statistics of Random Processes II. 2nd rev. and exp. edn. Springer. Translated by A. B. Aries. (Cited on page 148.)
McDonald, Robert, and Siegel, Daniel. 1986. The value of waiting to invest. Quart. J. Econ., 101(4), 707–728. (Cited on pages x, 77, and 88.)
McKean, Henry P. Jr., 1969. Stochastic Integrals. New York: Academic Press. (Cited on page 53.)
Øksendal, Bernt K. 2007. Stochastic Differential Equations: An Introduction with Applications. 6 edn. Berlin; New York: Springer. (Cited on pages 60 and 88.)
Ormeci, Melda, Dai, J. G., and Vande Vate, John H. 2008. Impulse control of Brownian motion: The constrained average cost case. Operations Research, 56, 618–629. (Cited on pages 126 and 134.)
Peskir, Goran, and Shiryaev, Albert N. 2006. Optimal Stopping and Free-Boundary Problems. Lectures in Mathematics. ETH Zürich. Birkhäuser Basel. (Cited on pages 88 and 154.)
Poor, H. Vincent, and Hadjiliadis, Olympia. 2008. Quickest Detection. Cambridge: Cambridge University Press. (Cited on page 8.)
Rogers, L. C. G., and Williams, David. 1987. Diffusions, Markov Processes and Martingales: Itô Calculus. Wiley Series in Probability and Mathematics Statistics, vol. 2. New York: John Wiley & Sons Ltd. (Cited on page 8.)
Ross, S.M. 1983. Stochastic Processes. New York: Wiley. (Cited on pages 98 and 104.)
Stokey, Nancy L. 2009. The Economics of Inaction. New Jersey: Princeton University Press. (Cited on page x.)
Wenocur, M. 1982. A production network model and its diffusion limit. Ph.D. thesis, Department of Statistics, Stanford University. (Cited on page 34.)
Wonham, W. 1964. Some applications of stochastic differential equations to optimal nonlinear filtering. SIAM J. Contr. Optimizat., 2(3), 347–369. (Cited on page 150.)

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.