Outline 00:00 - Intro 02:25 - Bachelier and the Théorie de la Spéculation 03:05 - Stochastic processes, Brownian motion, and the heat equation 09:45 - Poincaré's verdict, obscurity, and rediscovery 13:50 - Robert C. Merton: from hot rods to MIT 19:25 - Dynamic programming and Itô calculus 24:35 - Merton's portfolio problem as stochastic optimal control 31:10 - Options, dynamic hedging, and the Black–Scholes–Merton equation 39:50 - LTCM: the dream team 46:30 - August 1998: the crash 49:00 - Fat tails and the ten-sigma defense 51:40 - The ghosts of 2008 and echoes in the AI boom 54:00 - Robustness embraced at last: Hansen and Sargent 57:45 - Outro Links Bachelier's thesis, "Théorie de la Spéculation" (1900): https://www.numdam.org/item/10.24033/asens.476.pdf Courtault et al., "Louis Bachelier on the Centenary of Théorie de la Spéculation": https://doi.org/10.1111/1467-9965.00098 Merton's Nobel autobiography: https://www.nobelprize.org/prizes/economic-sciences/1997/merton/biographical/ Merton's MIT "Infinite History" interview: https://infinite.mit.edu/video/robert-c-merton-phd-%E2%80%9970/ Mandelbrot, "The Variation of Certain Speculative Prices": https://doi.org/10.1086/294632 Merton, "Optimum Consumption and Portfolio Rules in a Continuous-Time Model": https://doi.org/10.1016/0022-0531(71)90038-X Moehle & Boyd, "A Certainty Equivalent Merton Problem": https://doi.org/10.1109/LCSYS.2021.3111534 Brigo & Mercurio, "Interest Rate Models: Theory and Practice": https://doi.org/10.1007/978-3-540-34604-3 Armstrong, Brigo & Hanzon, "Optimal Projection Filters with Information Geometry": https://doi.org/10.1007/s41884-023-00108-x Hu & Zhou, "Constrained Stochastic LQ Control with Random Coefficients, and Application to Portfolio Selection": https://doi.org/10.1137/S0363012904441969 Black & Scholes, "The Pricing of Options and Corporate Liabilities": https://doi.org/10.1086/260062 Merton, "Theory of Rational Option Pricing": https://doi.org/10.2307/3003143 Merton, "Option Pricing When Underlying Stock Returns Are Discontinuous": https://doi.org/10.1016/0304-405X(76)90022-2 Scholes' Nobel lecture: https://www.nobelprize.org/prizes/economic-sciences/1997/scholes/lecture/ Merton's Nobel lecture: https://www.nobelprize.org/prizes/economic-sciences/1997/merton/lecture/ Markowitz, "Portfolio Selection": https://doi.org/10.2307/2975974 Michael Lewis, "Liar's Poker": https://en.wikipedia.org/wiki/Liar%27s_Poker Edwards, "Hedge Funds and the Collapse of Long-Term Capital Management": https://doi.org/10.1257/jep.13.2.189 Lowenstein, "When Genius Failed": https://en.wikipedia.org/wiki/When_Genius_Failed Taleb, "Statistical Consequences of Fat Tails": https://arxiv.org/abs/2001.10488 Taleb & West, "Working with Convex Responses: Antifragility from Finance to Oncology": https://doi.org/10.3390/e25020343 Taleb, "The Black Swan": https://en.wikipedia.org/wiki/The_Black_Swan:_The_Impact_of_the_Highly_Improbable Taleb, "Fooled by Randomness": https://en.wikipedia.org/wiki/Fooled_by_Randomness Man Group, "The AI Bubble: Hidden Risks and Opportunities": https://www.man.com/insights/the-ai-bubble Sen. Warren's remarks at the Vanderbilt Policy Accelerator: https://www.banking.senate.gov/newsroom/minority/warren-remarks-at-vanderbilt-policy-accelerator-event-highlighting-economic-and-financial-risks-of-potential-ai-crash Meng & Chen, "Artificial Intelligence and Systemic Risk": https://arxiv.org/abs/2604.03272 Doyle, "Guaranteed Margins for LQG Regulators": https://doi.org/10.1109/TAC.1978.1101791 Safonov & Athans, "Gain and Phase Margin for Multiloop LQG Regulators": https://doi.org/10.1109/TAC.1977.1101470 Hansen & Sargent, "Robust Control and Model Uncertainty": https://doi.org/10.1257/aer.91.2.60 Hansen & Sargent, "Wanting Robustness in Macroeconomics": http://www.tomsargent.com/research/wanting.pdf Support the show Podcast info Podcast website: https://www.incontrolpodcast.com/ Apple Podcasts: https://tinyurl.com/5n84j85j Spotify: https://tinyurl.com/4rwztj3c RSS: https://tinyurl.com/yc2fcv4y Youtube: https://tinyurl.com/bdbvhsj6 Facebook: https://tinyurl.com/3z24yr43 Twitter: https://twitter.com/IncontrolP Instagram: https://tinyurl.com/35cu4kr4 Acknowledgments and sponsors This episode was supported by the National Centre of Competence in Research on «Dependable, ubiquitous automation» and the IFAC Activity fund. The podcast benefits from the help of an incredibly talented and passionate team. Special thanks to L. Seward, E. Cahard, F. Banis, F. Dörfler, J. Lygeros, ETH studio and mirrorlake . Music was composed by A New Element.