Introduces stochastic control and mathematical modelling to researchers and graduate students in applied mathematics, mathematical economics, and non-linear PDE theory.
Introduces stochastic control and mathematical modelling to researchers and graduate students in applied mathematics, mathematical economics, and non-linear PDE theory.
Hiroaki Morimoto is a Professor in Mathematics at the Graduate School of Science and Engineering at Ehime University. His research interests include stochastic control, mathematical economics and finance and insurance applications, and the viscosity solution theory.
Inhaltsangabe
Part I. Stochastic Calculus and Optimal Control Theory: 1. Foundations of stochastic calculus 2. Stochastic differential equations: weak formulation 3. Dynamic programming 4. Viscosity solutions of Hamilton-Jacobi-Bellman equations 5. Classical solutions of Hamilton-Jacobi-Bellman equations Part II. Applications to Mathematical Models in Economics: 6. Production planning and inventory 7. Optimal consumption/investment models 8. Optimal exploitation of renewable resources 9. Optimal consumption models in economic growth 10. Optimal pollution control with long-run average criteria 11. Optimal stopping problems 12. Investment and exit decisions Part III. Appendices: A. Dini's theorem B. The Stone-Weierstrass theorem C. The Riesz representation theorem D. Rademacher's theorem E. Vitali's covering theorem F. The area formula G. The Brouwer fixed point theorem H. The Ascoli-Arzela theorem.
Part I. Stochastic Calculus and Optimal Control Theory: 1. Foundations of stochastic calculus 2. Stochastic differential equations: weak formulation 3. Dynamic programming 4. Viscosity solutions of Hamilton-Jacobi-Bellman equations 5. Classical solutions of Hamilton-Jacobi-Bellman equations Part II. Applications to Mathematical Models in Economics: 6. Production planning and inventory 7. Optimal consumption/investment models 8. Optimal exploitation of renewable resources 9. Optimal consumption models in economic growth 10. Optimal pollution control with long-run average criteria 11. Optimal stopping problems 12. Investment and exit decisions Part III. Appendices: A. Dini's theorem B. The Stone-Weierstrass theorem C. The Riesz representation theorem D. Rademacher's theorem E. Vitali's covering theorem F. The area formula G. The Brouwer fixed point theorem H. The Ascoli-Arzela theorem.
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