Bob Kertz
Professor Emeritus of Mathematics
Georgia Institute of Technology

phone: (404)-894-4311
fax: 404-894-4409
email: kertz@math.gatech.edu
office: Skiles 133B

EDUCATIONAL BACKGROUND:

B.S. 1968, U. of Chicago, Mathematics

M.S. 1969, Northwestern U., Mathematics

Ph.D. 1972, Northwestern U., Mathematics

CURRENT FIELDS OF INTEREST:

Have been working on probabilistic sequential decision models and inequalities for stochastic processes. Have developed universal sharp inequalities for several classes of processes by using constructive reduction, convexity, and recursion techniques (e.g., 'prophet' inequalities). Precise comparisons between several quantities in optimal stopping and extreme value theory have resulted. Have also proved existence results for optimal policies in several settings.

Have been investigating probabilistic sequential decision processes with special structures, including multiarmed bandit processes with monotonicity assumptions, and simulated annealing Markov chains and diffusions.

Have worked toward the analysis of various ordinary and partial differential equations through probabilistic techniques involving related stochastic process. Have special interests within the fields of discontinuous stochastic processes, random evolutions, and in areas of their application.

SAMPLE PUBLICATIONS:

"Largest-fit Selection of Random Sizes Under a Sum Constraint: Comparisons by Weak Convergence," co-authored with F. Boshuizen, pages 55-76 in Exploring Stochastic Laws, (1995), edited by A. V. Skorokhod and Yu.V. Borouskikh, VSP, Utrecht.

"Hyperbolic-Concave Functions and Hardy-Littlewood Maximal Functions," co-authored with U. R”sler, (1993), in the Proceedings of the AMS-IMS-SIAM Conference on Stochastic Inequalities, Edited by Y.L. Tong and M. Shaked, Institute of Mathematical Statistics Lecture Notes - Monograph Series, Hayward, California.

"Consistency and Continuity of Choice in a Sequence of Spot and Futures Markets," co-authored with D. C. Nachman, in Equilibrium Theory with Infinitely Many Commodities, (1992), edited by A. Khan and N. C. Yannelis, Springer-Verlag.

"Limit Theorems for Suprema, Threshold-Stopped Random Variables and Last Exits of i.i.d. Random Variables with Costs and Discounting, with Applications to Optimal Stopping," co-authored with D.P. Kennedy (1992) Advances in Applied Probability, 24, 241-266.

"Stochastic and Convex Orders and Lattices of Probability Measures, with a Martingale Interpretation," co-authored with U. R”sler, (1992), Israel Journal of Mathematics, 77, 129-164.