Resource-Based Spike Mitigation Stochastic Control Problems

Abstract

Resource-based spike mitigation stochastic control problems are a class of stochastic control problems, akin to inventory control problems or linear quadratic regulator (LQR) problems. These problems involve consuming a resource to mitigate large, fast losses to a primary state ("spikes"). These properties, included with stochastic elements, draw out a unique behavior where optimal control policies conserve resources during "lucky streaks" and spend the resources during "unlucky streaks." However, these problems often have too many time steps and states to compute an optimal control policy with dynamic programming. This thesis gives examples of such problems and demonstrates how to effectively approximate solutions using suboptimal control methods.