Risk Modeling

Most risk models in finance still trace their roots to Harry Markowitz’s 1952 portfolio theory. His formula for portfolio variance has become institutional orthodoxy, from asset managers’ spreadsheets to central bank macro-models. But what if the model’s foundations are missing a critical component of today’s noisy markets? Victor Olkhov’s recent paper makes a sharp yet mathematically grounded argument: Markowitz variance drastically underestimates or overestimates true portfolio risk when trade volumes fluctuate — which they almost always do. ...

“Don’t put all your eggs in one basket” has long been gospel in finance and risk management. But what if sometimes, the basket is the safer place? In a surprising twist on conventional wisdom, Léonard Vincent’s latest paper presents the one-basket theorem: a theoretical framework that proves diversification can increase risk under certain extreme but relevant conditions. Specifically, when dealing with heavy-tailed risks that have infinite mean — such as those found in insurance, operational risk, and even crypto markets — putting all your eggs in one basket may be the rational choice. ...

In financial engineering, pricing exotic options often boils down to estimating one number: the expected payoff under a risk-neutral measure. But what if we’re asking the wrong question? That’s the provocative premise of a recent study by Ahmet Umur Özsoy, who reimagines option pricing as a distributional learning problem, not merely a statistical expectation problem. By combining insights from Distributional Reinforcement Learning (DistRL) with classical option theory, the paper offers a fresh solution to an old problem: how do we properly account for tail risk and payoff uncertainty in path-dependent derivatives like Asian options? ...