Jump Diffusion

One of the most sacred assumptions in financial modeling is the existence of a traded risk-free asset. It anchors discounting, defines arbitrage boundaries, and supports the edifice of Black–Scholes. But what happens when you remove this pillar? Can we still price options, hedge risk, or extract information about funding conditions? In a striking extension of the Lindquist–Rachev (LR) framework, Ziyao Wang shows that not only is it possible — it may reveal financial dynamics that conventional models obscure. ...

Markowitz’s mean-variance portfolio theory has long served as a pillar of modern finance, but in its classical form, it assumes a serene world of continuous returns and static market regimes. This serenity, however, shatters when real-world markets swing between boom and bust, triggering sudden and severe asset price shocks. The new paper by Shi and Xu takes a bold step in modeling this turbulence by embedding regime-switching-induced stock price jumps directly into the mean-variance framework. ...