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Jim Primbs Consulting Associate Professor Department of Management Science and Engineering Stanford University
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Publications
Software
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Research Topics/Interests
My research interests are in developing new methods for quantitative finance and financial engineering from a control, systems, and optimization perspective.
Specific research topics include: Control Methods for Dynamic Hedging and Portfolio Optimization (especially in the presence of transaction costs and constraints), Receding Horizon Control/Model Predictive Control, Modeling of Market Dynamics, Optimization based Pricing Bounds for Options, Dynamic Hedging Analysis, Pricing in Segmented Markets |
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2011 ACC Tutorial Session: An Introduction to Option Trading from a Control Perspective
Slides from the ACC 2010 Special Session: From Operations to Finance: Opportunities for Control Theory and Application Control Systems Methods in Finance: Modeling and Optimal Trading
2008 CDC Tutorial Session: “Control and Finance”
2007 ACC Workshop, “An Introduction to Finance for Control Theorists”
Stanford-Tsukuba-WCQF Joint Workshop, March 8-10, 2007, Stanford.
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Publications
“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.
Stochastic Receding Horizon Control “ A Fast Algorithm for Stochastic Model Predictive Control with Probabilistic Constraints”. (with M. Shin, 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.
(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 “LQR and Receding Horizon Approaches to Multi-Dimensional Option Hedging under Transaction Costs”. (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.
“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.
(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 |
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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.
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Courses MS&E 142 Investment Science (Undergrad) MS&E 242 Investment Science (Grad) MS&E 345 Financial Engineering
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Graduate Students Qi Li: (MS&E 2004) Jeffrey Sadowsky (MS&E 2006) Chang Hwan Sung (MS&E 2006) Pete Meindl (MS&E 2006) Bjorgvin Sigurdsson (MS&E 2007) Luc Vuilleumier (ETH Zurich 2006, Diploma Thesis) Wilfred Wong (MS&E, 2010) Minyong Shin (AA, 2010) Joo Hyung Lee (EE) Li Xu (MS&E) |
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Resources by Students “On the Black-Scholes Equation: Various Derivations” by Manabu Kishimoto, MS&E 408 Term Paper, May 2008. |
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Education B.S. Math and Electrical Engineering, UC Davis, 1994 M.S. Electrical Engineering, Stanford, 1995 Ph.D. Control and Dynamical Systems, Caltech, 1999
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Contact information
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