On randomized stopping times

On Regression-Based Stopping Times

We study approaches that fit a linear combination of basis functions to the continuation value function of an optimal stopping problem and then employ a greedy policy based on the resulting approximation. We argue that computing weights to maximize expected payoff of the greedy policy or to minimize expected squared-error with respect to an invariant measure is intractable. On the other hand, c...

Lecture notes on Stopping Times

Markov chains are awesome and can solve some important computational problems. A classic example is computing the volume of a convex body, where Markov chains and random sampling provide the only known polynomial time algorithm. Arguably the most important question about a Markov chain is how long to run it until it converges to its stationary distribution. Generally, a chain is run for some fi...

Randomized stopping times and American option pricing with transaction costs

In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surp...

Randomized Stopping Times and Provably Secure Pseudorandom Permutation Generators

Conventionally, key-scheduling algorithm (KSA) of a cryptographic scheme runs for predefined number of steps. We suggest a different approach by utilization of randomized stopping rules to generate permutations which are indistinguishable from uniform ones. We explain that if the stopping time of such a shuffle is a Strong Stationary Time and bits of the secret key are not reused then these alg...

Randomized stopping times and coherent multiperiod risk measures