Sequential Design for Optimal Stopping Problems

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.Comment: 24 page

American Option Pricing: From PDE Numerical Solutions to Simulation-Based Methods and Reinforcement Learning.

An American call (put) option is a contract that gives the holder the right, but not the obligation, to buy (sell) one unit of an asset (typically, stock) at a prespecified price (called strike price) at any desired time before a preset expiration time of the contract. The associated option pricing problem plays an important role in modern financial markets and one way to solve this is by searching for the optimal exercise policy, i.e., find the optimal time to exercise so that maximal reward is achieved. In this thesis, we shall discuss the modern Least Square Policy Iteration Method to solve the American option pricing problem based on Reinforcement Learning and compare it to the method of the Longstaff-Schwartz Method and the Finite Difference Method

Pricing American Options by Exercise Rate Optimization

We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called optimal exercise regions, which consist of points in time and space at which a given option is exercised. In contrast, our method determines the exercise rates of randomized exercise strategies. We show that the supremum of the corresponding stochastic optimization problem provides the correct option price. By integrating analytically over the random exercise decision, we obtain an objective function that is differentiable with respect to perturbations of the exercise rate even for finitely many sample paths. The global optimum of this function can be approached gradually when starting from a constant exercise rate. Numerical experiments on vanilla put options in the multivariate Black-Scholes model and a preliminary theoretical analysis underline the efficiency of our method, both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates. Finally, we demonstrate the flexibility of our method through numerical experiments on max call options in the classical Black-Scholes model, and vanilla put options in both the Heston model and the non-Markovian rough Bergomi model

Emergency Management Training for Transportation Agencies

State transportation agencies have a variety of responsibilities related to emergency management. Field personnel manage events--from day-to-day emergencies to disasters--using the Incident Command System (ICS) as their organizational basis. At the headquarters level, the Emergency Operations Center (EOC) coordinates the use of resources across the department and its districts, with other state departments and agencies, and through the federal Emergency Support Function 1. District-level EOCs coordinate with the department. In extreme events, the transportation department may only be able to deliver limited essential services in austere conditions, so a continuity of operations/ continuity of government plan (COOP/COG) is essential. This research applied the principles of andragogy to deliver ICS field level training, EOC training and COOP/COG training to state transportation agency’s staff in all districts and at headquarters. The data supports the need for adult-oriented methods in emergency management training