Current research interests:

Prof. Kertz has been working on probabilistic sequential decision models and inequalities for stochastic processes. He has 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. He also proved existence results for optimal policies in several settings.

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

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