After graduating in 1979, Peter was a Senior Simulation Scientist at the Computer Modelling Group (CMG) in Calgary, where he developed petroleum reservoir simulation software. After leaving CMG, Peter was the founding President of software startup Dynamic Reservoir Systems (DRS), also in Calgary. DRS produced reservoir simulation software for PC's, using the then enormous amount of memory available (640K). DRS had three employees: a president and two vice-presidents. After selling out his shares in DRS (now owned by Duke ) in 1987, Peter joined the University of Waterloo, where he is now a Professor in the Cheriton School of Computer Science. Peter's current research focuses on Computational Finance. He is a member of the Editorial Board of Applied Mathematical Finance and the Journal of Computational Finance. During the years 2008-2013, he was the Editor-in-chief of the Journal of Computational Finance.
In recent years, Peter has also carried out research related consulting for such organizations as: SunLife of Canada, NOVA, the Electric Power Research Institute, Smithville Bedrock Remediation Corporation, Los Alamos National Laboratory, Oak Ridge National Laboratory, and HydroGeoLogic.
While at Waterloo, Peter has held such administrative positions as: Associate Chair Graduate Studies (1991-1993), Director of the Institute for Computer Research (1995-1998), Associate (Vice) Director of the Cheriton School of Computer Science (2002-2005), Scientific Director of the Institute for Quantitative Finance and Insurance (2006-2008), and Director (Infrastructure), Cheriton School of Computer Science (2009-11).
Peter is currently a director of Aquanty, a software startup specializing in integrated modelling of three dimensional surface/subsurface water flows. Aquanty specializes in simulating the impact of industrial activity and climate change on water resources.
Peter left CMG (the Computer Modelling Group) in 1985. About 15 years ago, shares of CMG were trading at about $0.05 (split adjusted). Look at the CMG share price. Peter thinks about this every day.
Email: paforsyt at uwaterloo dot ca
Snail Mail: David R. Cheriton School of Computer Science
University of Waterloo
200 University Ave. W
Waterloo, Ontario N2L 3G1
Voice: +1 519 888 4567 x34415
Fax: +1 519 885 1208
The Mathematics of making money.
Hedging your bets. An interview for the Mathematics Faculty Annual Report.
For a brief overview, click here.
If that's got you interested, here is a 16 page pdf file with more information that you can download. An introduction to Option Pricing.
For even more information, you can read the 80 page pdf file An introduction to Computational Finance without Agonizing Pain.
A short description of the Computational Finance Project.
Banks, Bonuses and Busts (pdf poster) A jaundiced view of the financial sector.
Hedging Your Bets (pdf poster).
Optimal Investment in a Pension Plan (pdf poster).
Optimal strategy: Guaranteed Minimum Withdrawal Benefit (GMWB) This pdf figure shows the optimal strategy for the holder of a GMWB guarantee. This is an example solution of an optimal stochastic control problem.
"The moral swamp that is retail brokerage corrodes the rest of the financial industry, and much of corporate America with it." William Bernstein, "Corporate Finance and Original Sin," Financial Analysts Journal, Volume 62:3 (2006) pages 20-23.
"You surprise me. That's singular, sir. I have generally found, in my experience, that it's their own money people are most particular about. I have seen people get rid of a good deal of other people's money, and bear it very well: very well indeed." From Little Dorrit, Charles Dickens
Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation under stochastic volatility
(May 19, 2015)
Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations
(March 19, 2015)
Long term asset allocation for the patient investor
(November 20, 2014)
An unconditionally monotone numerical scheme for the two factor uncertain volatility model
(Revised, May 10, 2015)
The existence of optimal bang-bang controls for GMxB contracts
(Journal Version: SIAM Journal on Financial Mathematics 6 (2015) 117-139.)
Better than pre-commitment mean-variance portfolio allocation strategies: a semi-self-financing Hamilton-Jacobi-Bellman equation approach
(Revised, June 28, 2015)
Convergence of the embedded mean-variance optimal points with discrete sampling
(to appear, Numerische Mathematik, 2015)
Continuous time mean-variance optimal portfolio allocation under jump diffusion: an numerical impulse control approach
(Journal Version: Numerical Methods for Partial Differential Equations 30 (2014) 664-698.)
Hedging costs for variable annuities under Regime Switching
Hidden Markov Models in Finance: Volume II, Springer International Series in Operations Research and Management. Edited by R. Mamon and R. Elliot, 2014, Chapter 6, pages 133-166.
Preservation of scalarization optimal points in the embedding technique for continuous time mean variance optimization
(Journal Version: SIAM Journal on Control and Optimization 52 (2014) 1527-1546.)
A Comparison of iterated optimal stopping and local policy iteration for American options under regime switching
(Journal Version: Journal of Scientific Computing 58 (2014) 409-430.)
An optimal stochastic control framework for determining the cost of hedging of variable annuities
(Journal Version: Journal of Economic Dynamics and Control 44 (2014) 29-53.)
Comparison between the mean variance optimal and mean quadratic variation optimal trading strategies
(Journal Version: Applied Mathematical Finance 20 (2013) 415-449.)
Inexact arithmetic considerations for direct control and penalty methods: American options under jump diffusion
(Journal Version: Applied Numerical Mathematics 72 (2013) 33–51.)
Iterative methods for solution of the singular control formulation of a GMWB pricing problem
(Journal Version: Numerische Mathematik 122 (2012) 133-167.)
Methods for pricing American options under regime switching
(Journal Version: SIAM Journal on Scientific Computing 33 (2011) 2144-2168.)
Numerical methods for nonlinear PDEs in finance
(Chapter 22, pages 503-528 in Handbook of Computational Finance, Edited by J.C. Duan, J. Gentle, W. Hardle, Springer, 2012.)
Combined fixed point and policy iteration for HJB equations in finance
(Journal Version: SIAM Journal on Numerical Analysis 50 (2012) 1849-1860.)
Comparison of mean variance like strategies for optimal asset allocation problems
(Journal Version: International Journal of Theoretical and Applied Finance 15:2 (2012) DOI: 10.1142/S0219024912500148)
Optimal trade execution: a mean-quadratic-variation approach
(Journal Version: Journal of Economic Dynamics and Control 36 (2012) 1971-1991)
Continuous time mean variance asset allocation: a time consistent strategy.
(Journal Version: European Journal of Operational Research 209 (2011) 184-201).
Analysis of a penalty method for pricing a Guaranteed Minimum Withdrawal Benefit (GMWB)
(Journal Version: IMA Journal of Numerical Analysis 32 (2012) 320-351.)
Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation
(Journal Version: Journal of Economic Dynamics and Control 34 (2010) 207-230).
A Hamilton Jacobi Bellman approach to optimal trade execution
(Journal Version: Applied Numerical Mathematics 61 (2011) 241-265)
Valuing the Guaranteed Minimum Death Benefit clause with partial withdrawals
(Journal Version: Applied Mathematical Finance 16 (2009) 451-496.)
Pricing hydroelectric power plants with/without operational restrictions: a stochastic control approach
(Book Chapter: Nonlinear Models in Mathematical Finance, Edited by M. Ehrhardt, Nova Science Publishers, 2008, pages 253-281)
The effect of modelling parameters on the value of GMWB guarantees
(Journal Version: Insurance: Mathematics and Economics 43 (2008) 165-173.)
Implications of a regime switching model on natural gas storage valuation and optimal operation.
(Journal Version: Quantitative Finance 10 (2009) 159-176.)
A numerical scheme for the impulse control formulation for pricing variable annuities with a Guaranteed Minimum Withdrawal Benefit (GMWB)
(Journal Version: Numerische Mathematik 109 (2008) 535-569.)
Maximal use of central differencing for Hamilton-Jacobi-Bellman PDEs in Finance
(Journal version: SIAM Journal on Numerical Analysis 46 (2008) 1580-1601)
A semi-Lagrangian approach for natural gas storage valuation and optimal operation
(Journal version: SIAM J. Scientific Computing 30 (2007) 339-368.)
Robust numerical valuation of European and American options under the CGMY process
(Journal Version: Journal of Computational Finance 10:4 (Summer:2007) 31-69.)
Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
(Journal Version: Journal of Computational Finance 11:2 (2007/2008: Winter) 1-44.)
Infinite reload options: pricing and analysis
(Journal Version: J. Computational Applied Mathematics 222 (2008) 54-81.)
Dynamic hedging under jump diffusion with transaction costs
(Journal Version: Operations Research 57 (2009) 541-559.)
Valuing guarantees on spending funded by endowments
(Journal Version: Canadian Applied Mathematics Quarterly 17 (2009) 661-701.)
Numerical solution of two asset jump diffusion models for option valuation
(Journal Version: Applied Numerical Mathematics 58 (2008) 743-782)
Hedging with a correlated asset: solution of a nonlinear pricing PDE
(Journal Version: Journal of Computational and Applied Mathematics 200 (2007) 86-115)
Calibration and hedging under jump diffusion
(Journal Version: Review of Derivatives Research 9 (2006) 1-35)
A semi-Lagrangian approach for American Asian options under jump diffusion
(Journal Version: SIAM J. Sci. Comp. 27 (2005) 315-345)
Numerical methods and volatility models for cliquet options
(Journal Version: Applied Mathematical Finance 13 (2006) 353-386)
Pricing methods and hedging strategies for volatility derivatives
(Journal Version: Journal of Banking and Finance 30 (2006) 409-431)
Convertible bonds with call notice periods
(IASTED conference on Financial Engineering and Applications, Banff, 2003)
A penalty method for American options with jump diffusion processes
(Journal Version: Numerische Mathematik, 97:2 (2004) 321-352.)
Robust numerical methods for contingent claims under jump diffusion processes
(Journal Version: IMA J. Num. Anal., 25 (2005) 87-112.)
Wireless network capacity investment
(Journal version: European Journal of Operational Research 176 (2007) 584-609)
Analysis of the stability of the linear boundary condition for the Black-Scholes equation
(Journal Version: J. Comp. Fin., 8:1 (Fall, 2004) 65-92)
The valuation of convertible bonds with credit risk
(Journal Version: J. Derivatives, 11 (Fall, 2003) 9-29.)
Hedging segregated fund guarantees
(Book Chapter Version: in The Pension Challenge: Risk Transfers and Retirement Income Security, Edited by Olivia Mitchell and Kent Smetters, Oxford University Press (2003), pages 214-237.)
Numerical convergence properties of option pricing PDEs with uncertain volatility
(Journal Version: IMA J. Num. Anal., 23 (2003) 241-267.)
Understanding the behaviour and hedging of segregated funds offering the reset feature
(Journal Version: North Amer. Act. J., 6 (2002) 107-125.)
Managing telecommunication networks under uncertainty
(Journal Version: IEEE Trans. Networks, 10 (2002) 579-588.)
Stochastic Simulations For Problems in Finance with Optimal Decisions PDF version ( 2Meg )
(Book Chapter Version: Computational Methods in Decision-making, Economics and Finance, Edited by E. Kontoghiorches, B. Rustem, S. Siokos, Kluwer Series in Applied Optimization, Kluwer, Amsterdam (2002) pages 269-294.)
Negative coefficients in two factor option pricing models
(Journal Version: J. Comp. Fin., 7:1 (Fall, 2003) 37-73 )
Remedies for non-smooth payoffs in option pricing
(Journal Version: J. Comp. Fin., 6:4 (Summer, 2003) 25-40.)
Quadratic convergence of a penalty method for valuing American options
(Journal Version: SIAM J. Sci. Comp., 23 (2002) 2095-2122.)
A numerical PDE approach for pricing callable bonds
(Journal Version: Appl. Math. Fin., 8 (2001) 49-77.)
Valuation of segregated funds: shout options with maturity extensions
(Journal Version: Insurance: Mathematics and Economics, 29 (2001) 1-21.)
An object oriented framework for valuing shout options on high performance computer architectures.
(Journal Version: J. Econ. Dyn. Control, 27 (2003) 1133-1161.)
Shout options: a framework for pricing contracts which can be modified by the investor
(Journal Version: J. Comp. Appl. Math., 134 (2001) 213-241.)
A finite volume approach for contingent claims valuation
(Journal Version: IMA J. Num. Anal. 21 (2001) 703-731.)
Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers.
(Journal Version: Appl. Num. Math. 36 (2001) 427-445.)
Convergence of lattice and PDE methods for valuing path dependent options using interpolation.
(Journal Version: Review of Derivatives Research, 5 (2002) 273-314.)
Discrete Asian barrier options
(Journal Version: J. Comp. Finance 3 (Fall, 1999) 41-68.)
Discrete Parisian and delayed barrier options: A general numerical approach
(Journal Version: Adv. Futures Options Research 10 (1999) 1-16.)
A finite element approach to the pricing of discrete lookbacks with stochastic volatility
(Journal Version: Appl. Math. Finance 6 (1999) 87-106.)
Undergraduate courses: introduction to scientific computing, numerical linear algebra, numeric computation for dynamical simulation, software system design and implementation. Graduate courses: numerical solution of partial differential equations, preconditioners for sparse matrices, numerical solution of nonlinear hyperbolic partial differential equations, computational finance.
I have a C++ version of the Watsit sparse matrix solver package (scaler only for now). The solver is based on a PCG-like method which uses an incomplete LU factorization preconditioner. Level or drop tolerance preconditioning can be specified. This package has been successfully tested on problems in CFD, 3-D linear elasticity, option pricing, semi-conductor device simulation, and multi-phase subsurface flow. You can download the pdf user manual.
You can download a pdf version of my full curriculum vitae.
Vienna day 1, Vienna day 2Back to the Scicom home page.
Last modified: January 15, 2014