Michael Harrison returns to an important topic in stochastic process theory, and illustrates its many influential applications in business and economics.
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.
1. Brownian motion; 2. Stochastic storage models; 3. Further analysis of Brownian motion; 4. Stochastic calculus; 5. Optimally stopping a Brownian motion; 6. Reflected Brownian motion; 7. Optimal control of Brownian motion; 8. Brownian models of dynamic inference; 9. Further examples; Appendix A. Stochastic processes; Appendix B. Real analysis.