Submitted Papers

Least Squares Monte Carlo and Pathwise Optimization for Merchant Energy Production.

with Selvaprabu Nadarajah and Nicola Secomandi

Under revision for the 3nd round review at Operations Research

Presented at MSOM iFORM SIG conference, 2021

[-]Abstract

[+]Abstract

We study merchant energy production modeled as a compound switching and timing option. The resulting Markov decision process is intractable. Least squares Monte Carlo combined with information relaxation and duality is a state-of-the-art reinforcement learning methodology to obtain operating policies and optimality gaps for related models. Pathwise optimization is a competing technique developed for optimal stopping settings, in which it typically provides superior results compared to this approach, albeit with a larger computational effort. We apply these procedures to merchant energy production. Employing pathwise optimization requires methodological extensions. We use principal component analysis and block coordinate descent in novel ways to respectively precondition and solve the ensuing ill-conditioned and large scale linear program, which even a cutting-edge commercial solver is unable to handle directly. Both techniques yield near optimal operating policies on realistic ethanol production instances. However, at the cost of both considerably longer run times and greater memory usage, pathwise optimization leads to substantially tighter dual bounds compared to least squares Monte Carlo, even when specified in a simple fashion, complementing it in this case. Thus, it plays a critical role in obtaining small optimality gaps. Our numerical observations on the magnitudes of these bound improvements differ from what is currently known. This research has potential relevance for other commodity merchant operations contexts and motivates additional algorithmic work in the area of pathwise optimization.

Quadratic Hedging of Futures Term Structure Risk in Merchant Energy Trading Operations.

with Nicola Secomandi

Under 1st round review at Operations Research

[-]Abstract

[+]Abstract

Merchant energy trading companies manage conversion assets to exploit price differences across time, space, and sources of energy in the face of energy futures term structure risk. Financial hedging of this risk is thus standard practice. Market incompleteness, such as limited futures liquidity, complicates the management of this activity. We apply quadratic hedging, a pragmatic approach to mitigate financial risk when markets are incomplete, to the management of term structure risk in real option models of merchant energy trading operations. We develop a model that, in contrast to known applications of this methodology, pools cash flows across dates, establish the structure of its optimal policy, which is intractable to obtain, and use it to propose a novel computationally efficient heuristic. This method is provably optimal under a martingale assumption for the futures curve evolution. Our technique performs near optimally in a realistic numerical study focused on natural gas storage in which this assumption does not hold, outperforming a benchmark that relies on it. The procedure put forth in this paper has potential applicability beyond this setting.

Working Papers

Pathwise Optimization based Reinforcement Learning Approach for Merchant Energy Operations.

with Selvaprabu Nadarajah and Nicola Secomandi

Draft Available

Presented at INFORMS 2020 and 2021

[+]Abstract

[-]Abstract

Pathwise optimization reinforcement learning (PRL) has been used to obtain high-quality bounds and control policies for Markov decision processes with rich informational structures, e.g., financial and real option models. PRL solves a sampled linear program (LP). However, the boundedness of this LP relies on the feasibility of terminal decisions, such as execution and abandonment in financial and real options, at each controllable state. The state-of-the-art approach in dealing with this LP also exhibits high per iteration computational complexity in complicated settings. These two limits restrict the applicability of PRL. We propose a pseudo-action scheme and a coordination decomposition and regression approach to deal with these two issues, respectively. The pseudo-action scheme deals with the unboundedness issue by adding artificial actions that belong to nonanticipated policies, i.e., policies that do not use future information. The coordinated decomposition (alternating direction method of multipliers) solves the dual of the sampled LP and recovers an associated primal solution by approximately enforcing complementary slackness via two-norm regression. This approach features lower per iteration computational complexity than the state-of-the-art method does. We conduct numerical studies with respective merchant energy storage and production modeled as real options. Our technique successfully extends PO to merchant energy storage, generating slightly better results than the benchmark method. In merchant energy production, our technique can solve both existing instances more efficiently compared to the state of the art method and new larger size ones that were out of reach, achieving near-optimal performance and dominating a standard competitor in terms of solution quality.

A Study of Non-Gaussian Processes for Merchant Energy Production.

with Anna Gambaro and Nicola Secomandi

Draft Available

[+]Abstract

[-]Abstract

Operation models for energy conversion assets typically employ Gaussian-based representations to capture the market dynamics. This approach facilitates the optimization of operational policies but is nevertheless at odds with empirical facts about energy and commodity prices, particularly the price’s “jump” behavior. Non-Gaussian processes better capture these features. We discuss this alternative modeling strategy in this empirical paper. Focusing on Levy processes and a natural gas storage setting, we numerically show that replacing a Gaussian-based term structure model with a Levy model substantially increases the optimal policy value. Further, we highlight the potential implications of using this approach to formulate energy and commodity operations models. Our work has broader relevance for modeling the dynamics of other market variables and operational quantities, such as exchange rates and demand forecasts

Work in Progress

A Constraint Aggregation and Disaggregation Method to Continuous Endogenous State Merchant Energy Operations.

with Selvaprabu Nadarajah and Nicola Secomandi

Data Driven Distributionally Robust Optimization for Merchant Energy Operations Models.

with Nicola Secomandi

Working with Levy Models in the Context of Energy Trading Operations.

with Nicola Secomandi

Improving the Dual Bound Generated by the Least Squares Monte Carlo method.

with Selvaprabu Nadarajah and Nicola Secomandi