Convex Stochastic Optimization Dynamic Programming and Duality in Discrete Time

This book studies a general class of convex stochastic optimization (CSO) problems that unifies many common problem formulations from operations research, financial mathematics and stochastic optimal control. We extend the theory of dynamic programming and convex duality to allow for a unified and simplified treatment of various special problem classes found in the literature. The extensions allow also for significant generalizations to existing problem formulations. Both dynamic programming and duality have played crucial roles in the development of various optimality conditions and numerical techniques for the solution of convex stochastic optimization problems.

- 1. Convex Stochastic Optimization.- 2. Dynamic Programming.- 3. Duality.- 4. Absence of a Duality Gap.- 5. Existence of Dual Solutions.

Teemu Pennanen is the Professor of Financial Mathematics, Probability and Statistics at King's College London. Before joining KCL, professor Pennanen worked as Managing Director at QSA Quantitative Solvency Analysts Ltd, with a joint appointment as Professor of Mathematics at the University of Jyvaskyl. His research interests include convex optimization, probability and statistics and their applications to operations research and financial economics. Pennanen has authored over 50 journal publications and he has been a consultant to a number of financial institutions including Bank of Finland, The State Pension Fund and Ministry of Social Affairs and Health.

Ari-Pekka Perkkiö is a senior assistant professor in Financial and Insurance Mathematics at the Department of Mathematics of Ludwig-Maximilians-Universität München. Before joining LMU, first as a junior professor, Perkkiö worked at Technische Universität Berlin and Aalto Universtiy. He has authored over 20 publications on optimization, variational analysis, probability theory, stochastic analysis and financial mathematics.