Jim Primbs

Jim Primbs

Assistant Professor

Department of Management Science and Engineering

Stanford University

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My research interests are in developing control theory (especially receding horizon control) and optimization methods for applications in quantitative finance and engineering. My current emphasis is on building financial engineering into a standard application area for the control community through research, education, and outreach.

Specific Research Interests:

Stochastic Receding Horizon Control

Financial Engineering Applications of Control Theory

Optimization based Methods for Derivative Pricing

Dynamic Hedging Analysis

Asset Pricing under Segmentation

Recent Research

Stochastic Receding Horizon Control

“Stochastic Receding Horizon Control of Constrained Linear Systems with State and Control Multiplicative Noise”. (with C. H. Sung; accepted to IEEE TAC)

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.

Financial Engineering Applications

“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)

We 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”. (Submitted)

In this work we formulate the problem of hedging a basket option (an option on a basket of underlying securities) as a constrained stochastic control problem. We 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”. (Submitted)

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; Revised for Applied Math Finance)

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.

Publications

Journal Papers, Conference Papers, Technical Reports, and Thesis

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) (Fall '07)

MS&E 242 Investment Science (Grad) (Fall ’07)

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