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...

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...

Owned by nobody and controlled by an almost immutable protocol the Bitcoin payment system is a platform with two main constituencies: users and profit seeking miners who maintain the system's infrastructure. The paper seeks to understand the economics of the system: How does the system raise...

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 propose a simple approach to dynamic multi-period portfolio choice with transaction costs that is tractable in settings with a large number of securities, realistic return dynamics with multiple risk factors, many predictor variables, and stochastic volatility. We obtain a closed-form...