Jim Primbs

My work in this area has ranged from developing new theoretical frameworks that connect receding horizon methods with control Lypunov functions, to robustness, stability and performance analysis, new computational methods, and advances for stochastic systems. My current interests are in the application of RHC/MPC methods to stochastic systems, with an emphasis on financial applications.

Control Systems Approach to Financial Engineering

My research in this area seeks to create opportunities for the use of control methods in financial engineering by developing control systems motivated formulations and solutions of finance problems. My work has included new RHC/MPC approaches to dynamic hedging, portfolio optimization, and index tracking problems that involve transaction costs and/or constraints, semi-definite programming methods for bounding option prices, dynamical systems modeling of the feedback effects of traders on price dynamics, dynamic hedging analysis tools, and a general framework for pricing in segmented markets.

News/Events

2010 ACC Workshop Proposal with B. Ross Barmish, “On the Basics of Stock Options: Control Paradigms, Research Directions, and Retirement Strategies”.

2009 ACC Workshop, “On Stock Market Trading and Portfolio Optimization: A Control Systems Perspective”

2008 CDC Tutorial Session: “Control and Finance”

“Control Methods for Financial Portfolios”, CDC Presentation Dec. 10, 2008, Cancun, Mexico.

“A Control Systems based Look at Financial Engineering”. (Draft) This is the tutorial paper that corresponds to the CDC presentation above. Please feel free to send me comments regarding it.

2007 ACC Workshop, “An Introduction to Finance for Control Theorists”

Stanford-Tsukuba-WCQF Joint Workshop, March 8-10, 2007, Stanford.

Stanford-Tsukuba Joint Workshop on Financial Engineering and Systems Management, March 2-3, 2006, Stanford.

Publications

Books

“The Factor Approach To Derivative Pricing: The BIG Picture in a little Book” (Draft)

This is a first (and rough) draft of a book on a simple approach to traditional derivative pricing. It assumes some familiarity with derivative pricing. The purpose of the book is to clearly explain the key underlying principle behind derivative pricing and to make it as accessible as possible, especially to an engineering audience. Please feel free to send me feedback about it.

Tutorials

“A Control Systems based Look at Financial Engineering”, (Draft)

This is a tutorial paper based on my CDC 2008 presentation in the “Control and Finance” tutorial session.

Recent Research

Stochastic Receding Horizon Control

NEW! “ A Fast Algorithm for Stochastic Model Predictive Control with Probabilistic Constraints”.

(with M. Shin, submitted to ACC 2010).

This paper develops a fast interior point algorithm for solving finite horizon stochastic control problems with probabilistic constraints by exploiting Riccati structure in the step direction calculation.

“Stochastic Receding Horizon Control of Constrained Linear Systems with State and Control Multiplicative Noise”.

(with C. H. Sung; accepted to IEEE TAC, 2009)

In this paper we develop a semi-definite programming based formulation of constrained stochastic receding horizon control. Furthermore, we characterize the stability, performance, and constraint satisfaction properties of this approach.

“A Soft Constraint Approach to Stochastic Receding Horizon Control”. (CDC 2007)

The paper develops a soft constraint approach to constrained stochastic receding horizon where constraint violations are severely penalized. We prove guaranteed stability properties of this approach.

Control Approach to Financial Engineering

NEW! “LQR and Receding Horizon Approaches to Multi-Dimensional Option Hedging under Transaction Costs”.

(Submitted to ACC 2010)

By sampling over paths and linearly parameterizing control actions, I formulate the dynamic hedging problem under transaction costs as a linear-quadratic control problem with constraints. This allows the use of receding horizon methods for its solution, demonstrating the great potential of control systems methodologies for problems of this type.

“Dynamic Spread Trading”. (with S-J. Kim and S. Boyd; Submitted)

This paper models the dynamic trading of multiple spreads and derives the optimal dynamic trading strategy. Extensive tests are run on four pairs of S&P 500 stocks that show that performance is significant and robust to realistic transaction costs.

“Optimization based Option Pricing Bounds via Piecewise Polynomial Super- and Sub-Martingales”. (ACC 2008)

I construct piecewise polynomial super- and sub-martingales associated with an option pricing problem. We use derived conditions for super- and sub-martingales in a novel sum-of-squares optimization problem to compute bounds on the option price. A numerical example illustrates the computations.

“Optimal Pairs Trading: A Stochastic Control Approach”

(with S. Mudchanatongsuk and W. Wong; ACC 2008)

We model the problem of optimally trading pairs as a stochastic control problem and derive a closed form solution under our assumptions. The results are tested on a simulated example and maximum likelihood estimation formulas are given as well.

“Dynamic Hedging of Basket Options under Proportional Transaction Costs using Receding Horizon Control”.

(Accepted to International Journal of Control, 2009)

In this work I formulate the problem of hedging a basket option (an option on a basket of underlying securities) as a constrained stochastic control problem. I then solve the problem using methods from constrained stochastic receding horizon control.

“An SDP Relaxation of Arbitrage Pricing Bounds based on Option Prices and Moments”. (Accepted to Journal of Optimization Theory and Applications. To appear Jan. 2010.)

This work develops a semi-definite programming (SDP) optimization problem that computes upper and lower bounds on the absence of arbitrage bounds of an option price when only moment information and the prices of other options at different strikes and expirations in known.

“Trader Behavior and its Effect on Asset Price Dynamics”.

(with Muruhan Rathinam; Applied Math Finance, 2009)

We model the behavior of traders as a continuous time discrete event model, and derive sde’s for aggregate behavior and price dynamics via diffusion limits. This allows us to explore the effects of trading strategies such as value, momentum, and hedging on price dynamics.

More Publications

Chronological

By Subject

Financial Engineering Software

The FinGroup Toolset is a set of 4 Matlab Toolboxes (Financial Statistics, Derivative Pricing, Lattice, Hedging Analysis) designed to facilitate computation in financial engineering.

Download the FinGroup Toolset.

Courses

MS&E 142 Investment Science (Undergrad)

MS&E 242 Investment Science (Grad)

MS&E 345 Financial Engineering (Winter ’06)

Past: Engr 60 Engineering Economy (Fall '02)

Graduate Students

Qi Li: (MS&E 2004) Essays on Asset Pricing, Consumption and Wealth

Jeffrey Sadowsky (MS&E 2006) Learning by Investing with Market and Technical Uncertainty: A Real Options Approach

Chang Hwan Sung (MS&E 2006) Applications of Modern Control Theory in Portfolio Optimization

Pete Meindl (MS&E 2006) Portfolio Optimization and Dynamic Hedging with Receding Horizon Control, Stochastic Programming, and Monte Carlo Simulation

Bjorgvin Sigurdsson (MS&E 2007) Pricing Models for Inflation Derivatives