Mathematical Finance Manifesto

Keith A. Lewis

June 4, 2024

Abstract
Work remains to be done.

Mathematical Finance has made Nobel Prize winning advances since the 1950’s, but there is more to do.

Review

Markowitz

Black-Merton Scholes

Stephen Ross

Linzberger …

Critique

Continuous time.

Implicit assumptions. Optimization. Self-financing.

Lack of knobs.

Bid-ask spread.

Entities.

Dynamic hedging and cash flows.

The future

Clear trajectory.

Monte Carlo simulation.

Realtime analytics.

Pivot tables. Reporting.