Many financial markets operate as electronic limit order books under a price-time priority rule. In this setting, among all resting orders awaiting trade at a given price, earlier orders are prioritized for matching with contra-side liquidity takers. This creates a technological arms race among...

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the...

We introduce the pathwise optimization (PO) method, a new convex optimization procedure to produce upper and lower bounds on the optimal value (the "price") of a high-dimensional optimal stopping problem. The PO method builds on a dual characterization of optimal stopping problems as...