Sutra

The Jump-Diffusion Smile

What option markets remember that Black-Scholes forgets

The Black-Scholes model prices every strike with one volatility, yet listed markets have priced a persistent skew since October 1987. This article walks through Merton's jump-diffusion extension, shows how a small probability of a large jump reproduces the observed smile, and explains why the smile's shape is best read as the market's memory of crashes.

Daniel Okafor · Jul 19, 2026 · 1 min read

Paper

Mortality Improvement Models After the Pandemic

Meera Krishnan · Jul 23, 2026 · 2 min read

Paper

Attention Is Not All You Need: The Case for Hybrid Architectures

Tomás Aguiar · Jul 27, 2026 · 2 min read

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Essay

Rohan Yashraj Gupta

The actuarial profession is undergoing one of the most significant transformations in its history. Advances in artificial intelligence, machine learning, cloud computing, automation, and software engineering are fundamentally changing how insurers assess risk, make decisions, and deliver value. The modern actuary is no longer expected to be solely an expert in mathematics and statistics but also a technology strategist capable of designing intelligent, scalable, and trustworthy solutions.

Rohan Yashraj Gupta · Jul 30, 2026 · 6 min read

PaperArtificial Intelligence

Attention Is Not All You Need: The Case for Hybrid Architectures

Transformer attention scales quadratically with context length, and a decade of workarounds has produced diminishing returns. This paper surveys state-space models, linear attention, and hybrid architectures, and argues that the frontier is shifting from pure attention toward mixed designs that route information through cheaper structured operators. We review the empirical evidence and identify where hybrids currently fail.

Tomás Aguiar · Jul 27, 2026 · 2 min read

PaperActuarial Science

Mortality Improvement Models After the Pandemic

The pandemic years put a discontinuity into every national mortality series that stochastic improvement models were never designed to absorb. This paper examines how the Lee-Carter family behaves when 2020-2022 data is included naively, compares exclusion, dummy-variable, and regime-switching treatments, and offers practical guidance for pricing and reserving actuaries who must choose a treatment now.

Meera Krishnan · Jul 23, 2026 · 2 min read

ArticleFinance & Economics

The Jump-Diffusion Smile

Daniel Okafor · Jul 19, 2026 · 1 min read

TutorialSoftware Engineering

Type-Driven Refactoring in Practice

Large refactors fail when they depend on human attention across hundreds of call sites. This tutorial demonstrates a workflow that turns the TypeScript compiler into the driver: make the desired end state impossible to misuse, let the type errors enumerate the work, and land the change in mechanical, reviewable steps.

Hana Yoshida · Jul 15, 2026 · 2 min read

ArticleScience & Medicine

What Antibiotics Taught Us About Incentives

Antibiotic resistance is usually told as a biology story, but its persistence is an economics story. A new antibiotic is most valuable to society when it is used least, which destroys the revenue model that funds drug development. This article traces how that incentive inversion emptied the antibiotic pipeline and evaluates the subscription-style reforms now being trialled.

Hana Yoshida and Daniel Okafor · Jul 10, 2026 · 2 min read