Damon Petersen

Working Papers

Central Bank Balance Sheet and Treasury Market Disruptions, R&R Journal of Finance (with Adrien D'Avernas and Quentin Vandeweyer)

Presented at the New York Fed, Federal Reserve Board, Harvard (HBS), NYU Stern, Chicago Booth, European Central Bank, Princeton, London School of Economics, Bank of France, AFA, NBER SI, Stockholm School of Economics, CESifo, UCLA, Bank of Canada

This paper presents a dynamic asset pricing model of Treasury bonds with banks subject to both capital and liquidity requirements. Capital requirements and households’ preference for money-like assets push non-banks to be the primary holders of Treasuries, thereby exposing Treasury yields to funding shocks originating in repo markets. When holding sufficient reserves, banks mitigate those shocks by lending in repo when the funding supply tightens. When reserves are scarce, banks stop lending. Repo rates and Treasury yields spike up to reflect those funding imbalances. Our model highlights the key role of both sides of the central bank's balance sheet as well as agents' anticipation about the duration of shocks and policy intervention in explaining observed Treasury market disruptions.

A Solution Method for Continuous-Time General Equilibrium Models (with Adrien D'Avernas and Quentin Vandeweyer) [python library]

We propose an algorithm capable of solving a general class of continuous-time asset pricing models, including heterogeneous agent models, in a fast and standardized way. These models require the solution of a Hamilton-Jacobi-Bellman equation for each agent coupled with a system of algebraic equations. We rely on a finite difference algorithm and show how using a Stern-Brocot Tree decomposition as advocated by Bonnans, Ottenwaelter, and Zidani (2004) allows for fast and stable convergence in settings with up to two endogenous and stochastic state variables. We provide an open source software package, PyMacroFin, that includes an object-oriented interface for model definition and solution for any model in this general class.

Publications: Optimization & Engineering

Optimal combined long-term facility design and short-term operational strategy for CHP capacity investments, Energy (with Jose Mojica, Brigham Hansen, Kody Powell, and John Hedengren)

This paper develops an optimization framework to jointly optimize capital investment and operations in a district energy system. We formulate capacity planning as a dynamic optimal control problem considering both operational modes and discrete capital investment decisions. The plant is modified by the dynamic optimization over a 30 year horizon to maximize profitability. The combined optimal controller and capital investment planner solves a large scale mixed integer nonlinear programming (MINLP) problem to provide the timing and size of the capacity investment (30 year outlook) and also guidance on the mode of operation (1 h time intervals). The optimizer meets optimal economic, environmental, and regulatory constraints with the suggested design and operational guidance with daily cyclical load following of heat and electricity demand.

Integrated scheduling and control in discrete-time with dynamic parameters and constraints, Computers & Chemical Engineering (with Logan Beal, David Grimsman, Sean Warnick, and John Hedengren)

Integrated scheduling and control (SC) seeks to unify the objectives of the various layers of optimization in manufacturing. This work investigates combining scheduling and control using a nonlinear discrete-time formulation, utilizing the full nonlinear process model throughout the entire horizon. This discrete-time form lends itself to optimization with time-dependent constraints and costs. An approach to combined SC is presented, along with sample pseudo-binary variable functions to ease the computational burden of this approach. An initialization strategy using feedback linearization, nonlinear model predictive control, and continuous-time scheduling optimization is presented. The formulation is applied with a generic continuous stirred tank reactor (CSTR) system in open-loop simulations over a 48-h horizon and a sample closed-loop implementation. The value of time-based parameters is demonstrated by applying cooling constraints and dynamic energy costs of a sample diurnal cycle, enabling demand response via combined scheduling and control.

Combined Noncyclic Scheduling and Advanced Control for Continuous Chemical Processes, Processes (with Logan Beal, Derek Prestwich, Sean Warnick, and John Hedengren)

A novel formulation for combined scheduling and control of multi-product, continuous chemical processes is introduced in which nonlinear model predictive control (NMPC) and noncyclic continuous-time scheduling are efficiently combined. A decomposition into nonlinear programming (NLP) dynamic optimization problems and mixed-integer linear programming (MILP) problems, without iterative alternation, allows for computationally light solution. An iterative method is introduced to determine the number of production slots for a noncyclic schedule during a prediction horizon. A filter method is introduced to reduce the number of MILP problems required. The formulation’s closed-loop performance with both process disturbances and updated market conditions is demonstrated through multiple scenarios on a benchmark continuously stirred tank reactor (CSTR) application with fluctuations in market demand and price for multiple products. Economic performance surpasses cyclic scheduling in all scenarios presented. Computational performance is sufficiently light to enable online operation in a dual-loop feedback structure.

Combined model predictive control and scheduling with dominant time constant compensation, Computers & Chemical Engineering (with Logan Beal, Junho Park, Sean Warnick, and John Hedengren)

Linear model predictive control is extended to both control and optimize a product grade schedule. The proposed methods are time-scaling of the linear dynamics based on throughput rates and grade-based objectives for product scheduling based on a mathematical program with complementarity constraints. The linear model is adjusted with a residence time approximation to time-scale the dynamics based on throughput. Although nonlinear models directly account for changing dynamics, the model form is restricted to linear differential equations to enable fast online cycle times for large-scale and real-time systems. This method of extending a linear time-invariant model for scheduling is designed for many advanced control applications that currently use linear models. Simultaneous product switching and grade target management is demonstrated on a reactor benchmark application. The objective is a continuous form of discrete ranges for product targets and economic terms that maximize overall profitability.

Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes, Processes (with Logan Beal, Guilherme Pila, Brady Davis, Sean Warnick, and John Hedengren)

Performance of integrated production scheduling and advanced process control with disturbances is summarized and reviewed with four progressive stages of scheduling and control integration and responsiveness to disturbances: open-loop segregated scheduling and control, closed-loop segregated scheduling and control, open-loop scheduling with consideration of process dynamics, and closed-loop integrated scheduling and control responsive to process disturbances and market fluctuations. Progressive economic benefit from dynamic rescheduling and integrating scheduling and control is shown on a continuously stirred tank reactor (CSTR) benchmark application in closed-loop simulations over 24 h. A fixed horizon integrated scheduling and control formulation for multi-product, continuous chemical processes is utilized, in which nonlinear model predictive control (NMPC) and continuous-time scheduling are combined.

Works in Progress

Reaching for Yield: Monetary Policy and the Cross-section of Returns (with Nordine Abidi, Ixart Flores, Christoph Kaufmann, and Quentin Vandeweyer)