Peter A. Forsyth

Professor, BSc (Western Ontario 1975), MSc (Australian National 1977), PhD (Western Ontario 1979)

Personal History

After graduating in 1979, Peter was a Senior Simulation Scientist at the Computer Modelling Group (CMG) in Calgary, where he developed petroleum reservoir analytics. After leaving CMG, Peter was the founding President of software startup Dynamic Reservoir Systems (DRS), also in Calgary. DRS produced reservoir simulation software for desktop workstations, using the then enormous amount of RAM memory available (640K). DRS had three employees: a president and two vice-presidents. After selling out his shares in DRS in 1987, Peter joined the University of Waterloo, where he was a Professor in the Cheriton School of Computer Science. After 29 years, Peter officially retired from Waterloo on November 1, 2016, and is now a Professor Emeritus. Life continues on pretty much as before, except that now he does not have the joy of attending committee meetings, which is one of the highlights of being a professor.

Peter's current research focuses on Computational Finance. He was a member of the Editorial Boards of Applied Mathematical Finance (2003-2023) and the Journal of Computational Finance (2004-2023). 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.

Peter's research has been funded by such organizations as: Neuberger Berman, the Royal Bank of Canada, Scotiabank, Credit Suisse, Tata Consultancy Services, Morgan Stanley, ITO33, Bell Canada, and the Global Risk Institute.

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. Aquanty specializes in integrated modelling of three dimensional surface/subsurface water flows. These simulations forecast the impact of industrial activity and climate change on water resources.

Peter left CMG (the Computer Modelling Group) in 1985. About 25 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.

Office: Davis Center 3622 Map to Davis Center Lobby

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

Fax: +1 519 885 1208

Research Expertise

Corona Virus SEIR Model

What is Computational Finance?

Video: The nastiest hardest problem in finance Recent talk at the Fields Institute: Decumulation Strategies for DC Pension Plans

Video: Bankers, Bonuses and Busts

For even more information, you can read the 120 page pdf file An introduction to Computational Finance without Agonizing Pain.

Audio and slides for: Multi-period mean-variance asset allocation

Press Releases

Constant weight vs. glide path ETFs

Machine-learning earnings: Novel approach triples investment success


The Canasta Strategy. (January 6, 2021)

If we priced tickets fairly, we'd be out of business. (March 22, 2019)

To equal weight or not to equal weight: that is the question. (January 22, 2019)

Bonds in a balanced portfolio: long term or short term? (October, 2018)

Making bets with other people's money (August, 2018)

Our clients would never know the difference anyway (July 20, 2018)

Picking up dollar bills in front of a steam roller (June18, 2018)

You can't go faster than the speed of light and the no-arbitrage condition (May 15, 2018)

White Papers

Is rebalancing bad for your wealth? (June 6, 2024)

A buy and hold portfolio loses diversification (December 12, 2023)

What's LDI got to do with it? (January 18, 2023)

Asset Allocation During High Inflation Periods: A Stress Test (June 16, 2022)

Decumulation of Defined Contribution Pension Plans: the canasta strategy (April 29, 2022)

Target Date Funds: a bad idea whose time has come (March 28, 2022)

Equal Weight vs Capitalization Weight Indexs (an update) (March 1, 2022)

Optimizing Retirement Income (April 30, 2021)

Target Wealth: a new approach to the retirement challenge (July 2019)

Target Wealth: A Better Bet for Achieving Wealth Goals, (American Association of Independent Investors (AAII) Journal, October 2017) (pdf version) or (HTML version)

Target Wealth: The Evolution of Target Date Funds or (SSRN version)

A Target GDP Approach to Risk and Return in Climate Change Policy

Are target date funds dinosaurs? Failure to adapt can lead to extinction.

Defined Benefit Plans are Disappearing

Variable Annuities: Fees too High or Too Low?

Defined Benefit Plans: Optimistic Valuation (Are you listening University of Waterloo pension committee members?)

Wishful Thinking About the Risk of Stocks in the Long Run: Consequences for Defined Contribution and Defined Benefit Retirement Plans

Bitcoin Exchange Traded Products (ETP)

''Though we're merit neutral, I'd note that the underlying assets in the metals ETPs have consumer and industrial uses, while in contrast bitcoin is primarily a speculative, volatile asset that’s also used for illicit activity including ransomware, money laundering, sanction evasion, and terrorist financing.'' Gary Gensler, Chairman SEC (January 10, 2024).

Retirement planning

''Play the long game. A retirement income plan should be based on planning to live, not planning to die. A long life will be expensive to support, and it should take precedence over death planning.'' Wade Pfau, Journal of Financial Counseling and Planning (2018) Vol 29:1, pages 114-120.

Will another bank fail? (Silicon Valley Bank)

''This view is largely based on the archaic idea that public companies are run for the benefit of their owners, the shareholders. They are not. They are run for the benefit of the people who are doing the running, that is, the management team." Robert Armstrong, The Financial Times (March 14, 2023).

Is it Time to Imvest in Alternative Assets, Private Equity, Bitcoin...?

''The history of the trade cycle had taught me that a period of a low rate of return on investments inexorably leads toward irresponsible investment. ... People won’t take 2% and cannot bear a loss of income. Instead, they invest their careful savings in something impossible - a canal to Kamchatka, a railway to Watchet, a plan for animating the Dead Sea." Walter Bagehot , Editor of The Economist 1861-1877.

A Sobering Thought

"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.

Charles Dickens had it right

"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

A comment about Donald Trump, 1993

"Mr. Donald Trump is said not to be broke; he was, however, described in recent news accounts as having negative net worth. These distinctions are no doubt important in the world of finance." From A short history of financial euphoria, (1993) by John Kenneth Gailbraith.

Market Meltdown 2008-2009

Are bankers popular?


List of recent journal publications

Technical Reports:

Please quote the final journal version instead of the technical report version.

Computing Optimal Multi-period 130/30 Portfolios: A Neural Network Framework
(January 31, 2024)

Machine learning and Hamilton-Jacobi-Bellman equation for optimal decumulation: a comparison study or arxiv version
(June 29, 2023)

Optimal asset allocation in a high inflation regime: a leverage-feasible neural network approach or arxiv version
(to appear, Quantitative Finance, 2024)

A parsimonious neural network approach to solve portfolio optimization problems without using dynamic programming or arxiv version
(Revised, December 6, 2023)

Across-time risk-aware strategies for outperforming a benchmark
(Journal Version: European Journal of Operational Research 313:2 (2024) 776-800.)

Optimal performance of a tontine overlay subject to withdrawal constraints Gold Open Access, or preprint version
(Journal Version: ASTIN Bulletin 54 (2024) 94-128.)

Multi-period mean expected-shortfall strategies: "cut your losses and ride your gains"
(Journal Version: Applied Mathematical Finance 29:5 (2022) 402-438.)

Beating a constant weight benchmark: easier done than said
(Journal Version: International Journal of Theoretical and Applied Finance (2023) paper 2350011 (electronic) ).

An ε-monotone Fourier method for Guaranteed Minimum Withdrawal Benefit as a continuous impulse control problem
(June 4, 2022)

Beating a benchmark: dynamic programming may not be the right numerical approach
(Journal Version: SIAM Journal on Financial Mathematics 14:2 (2023) 407-451.)

Short term decumulation strategies for underspending retirees
(Journal version: Insurance: Mathematics and Economics 102 (2022) 56-74.)

A data-driven neural network approach to dynamic factor investing with transaction costs
(August 20, 2021)

Optimal control of the decumulation of a retirement portfolio with variable spending and dynamic asset allocation
(Journal Version: ASTIN Bulletin 51:3 (2021) 905-938.)

Two stage decumulation strategies for DC plan investors
(Journal Version: International Journal of Theoretical and Applied Finance 24:1 (2021) Article 2150007, 1-31)

A stochastic control approach to defined contribution plan decumulation: the nastiest, hardest problem in finance''
(Journal Version: North American Actuarial Journal 26:2 (2022) 227-252)

Optimal asset allocation for outperforming a stochastic benchmark target
(Journal Version: Quantitative Finance 22:9 (2022) 1595-1626)

Practical investment consequences of the scalarization parameter formulation in dynamic mean-variance portfolio optimization
(Journal Version: International Journal of Theoretical and Applied Finance 24:5 (2021) Article 2150029, 1-49)

Optimal dynamic asset allocation for DC plan accumulation/decumulation: Ambition-CVAR
(Journal Version: Insurance: Mathematics and Economics 93 (2020) 230-245.)

On the distribution of terminal wealth under dynamic mean-variance optimal investment strategies
(Journal Version: SIAM Journal on Financial Mathematics 12 (2021) 566-603)

Optimal asset allocation for DC pension decumulation with a variable spending rule
(Journal Version: ASTIN Bulletin 50:2 (2020) 419-447.

The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors
(Journal Version: European Journal of Operational Research 289:2 (2021) 774-792)

Multi-period mean-CVAR asset allocation: is it advantageous to be time consistent?
(Journal Version: SIAM Journal on Financial Mathematics 11:2 (2020) 358-384.)

Defined Contribution Pension Plans: Who Has Seen the Risk?
(Journal Version: Journal of Risk and Financial Management, 12:2 (2019) (electronic, open access). )

Mean-Quadratic Variation Portfolio Optimization: A desirable alternative to Time-consistent Mean-Variance Optimization?
(Journal Version: SIAM Journal on Financial Mathematics 10:3 (2019) 815-856.)

A Data Driven Neural Network Approach to Optimal Asset Allocation for Target Based Defined Contribution Pension Plans
(Journal Version: Insurance: Mathematics and Economics 86 (2019) 189-204.)

Management of portfolio depletion risk through optimal life cycle asset allocation
(Journal Version: North American Actuarial Journal 23:3 (2019) 447-468.)

Climate Games: Who's on first? What's on second?
(Journal Version: l'Actualite Economique 95:2-3 (2019) 287-322.)

Strategic interactions and uncertainty in decisions to curb greenhouse gas emissions
(Journal Version: Frontiers of Economics in China 16:2 (2021) 214-262)

Time-consistent mean-variance portfolio optimization: a numerical impulse control approach
(Journal Version: Insurance: Mathematics and Economics 83 (2018) 9-28.)

ε-Monotone Fourier Methods for Optimal Stochastic Control in Finance
(Journal Version: Journal of Computational Finance 22:4 (2019) 25-71.)

Optimal Asset Allocation for Retirement Savings: Deterministic vs. Time Consistent Adaptive Strategies
(Journal Version: Applied Mathematical Finance 26:1 (2019) 1-37.)

Dynamic Mean Variance Asset Allocation: Tests for Robustness
(Journal version: International Journal of Financial Engineering 4:2 (2017) 1750021 (electronic).)

Robust Asset Allocation for Long-Term Target-Based Investing
(Journal version: International Journal of Theoretical and Applied Finance 20:3 (2017) 1750017 (electronic) )

Weakly chained matrices and impulse control
(Journal version: SIAM Journal on Numerical Analysis 54 (2016) 1341–1364.)

The 4% strategy revisited: A pre-commitment optimal mean-variance approach to wealth management
(Journal Version: Quantitative Finance 17 (2017) 335-351).

Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation under stochastic volatility
(Journal Version: Journal of Computational Finance 20:1 (2016) 1-37)

Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations
(Journal version: Applied Numerical Mathematics 103 (2016) 27-47.)

An unconditionally monotone numerical scheme for the two factor uncertain volatility model
(Journal Version: IMA Journal on Numerical Analysis 37 (2017) 905-944.)

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
(Journal Version: European Journal of Operational Research, 250 (2016) 827-841.)

Convergence of the embedded mean-variance optimal points with discrete sampling
(Journal Version: Numerische Mathematik 132 (2016) 271-302.)

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 (2007) 31-69.)

Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
(Journal Version: Journal of Computational Finance 11:2 (2007) 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.)

Courses Taught

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.

C++ Iterative Sparse Matrix Solver

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.

More information?

You can download a pdf version of my full curriculum vitae.

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Last modified: June 10, 2022