Randomized Optimal Stopping Algorithms and Their Convergence Analysis

On the rates of convergence of simulation based optimization algorithms for optimal stopping problems

In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large deviation theory for the increments of empirical processes, we derive optimal convergence rates and show that they can not be improved in general. The rates derived ...

Monte Carlo Algorithms for Optimal Stopping and Statistical Learning

We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation inequalities for suprema of empirical processes to derive consistency criteria, and to estimate the co...

Constrained Optimal Synthesis and Robustness Analysis by Randomized Algorithms

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order statistics is associated with certain constraints. In particular, we derive an inequality on distribution for related order statistics. Moreover, we also propos...

Periodic Oscillations in the Analysis of Algorithms and Their Cancellations

A large number of results in analysis of algorithms contain fluctuations. A typical result might read “The expected number of . . . for large n behaves like log2 n + constant + delta(log2 n), where delta(x) is a periodic function of period one and mean zero.” Examples include various trie parameters, approximate counting, probabilistic counting, radix exchange sort, leader election, skip lists,...

Optimal Parallel Randomized Algorithms for . . .