Continuous-time models give sharper results and drop quadratic utility.

Evidence

Compared with “discrete-time” models, “the continuous-time models are mathematically more complex,” says Merton. He quickly became convinced, however, that “the derived results of the continuous-time models were often more precise and easier to interpret than their discrete-time counterparts” (Merton 1998, pp. 18-19). His “intertemporal” Capital Asset Pricing Model (Merton 1973b), for example, did not necessitate the “quadratic utility” assumption of the original. — Donald MacKenzie, An Engine, Not a Camera, 594

Categorization

• XREF: The pattern — more math models yield cleaner, more usable results — is core to how the performativity thesis proceeds throughout the book. — connects to: Black-Scholes is a continuous-time limit of the binomial model — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1289; Mean-variance portfolio theory requires the restrictive quadratic utility assumption. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 588; Time-dependent d prime is needed because trial outcomes resolve at different times

Broader Connections

• Mean-variance portfolio theory requires the restrictive quadratic utility assumption. #corroborates (0.85) — Donald MacKenzie, An Engine, Not a Camera, 588
• Black-Scholes is a continuous-time limit of the binomial model #qualifies (0.75) — Donald MacKenzie, An Engine, Not a Camera, 1289
• Time-dependent d prime is needed because trial outcomes resolve at different times #exemplifies (0.72)