Syllabus
Mathematical Foundations of Modern Finance · Graduate Finance
Course description
A single-semester graduate treatment of the mathematics of modern finance, taught as one integrated system rather than a sequence of disconnected topics. The course develops, in order, the seven primitives of the field — uncertainty, information, value, time, decision, risk, and aggregation — and shows how the same state-price mathematics that prices a contingent claim also disciplines portfolio choice, the timing of irreversible commitments, risk measurement, and equilibrium. Each chapter opens with a decision facing the Meridian Endowment investment committee and closes with a hands-on laboratory module.
Prerequisites
- Multivariable calculus and linear algebra
- Probability at the level of a first rigorous course (random variables, expectation, conditioning)
- Working programming ability (the companion laboratory is in Python; no prior finance required)
Measure-theoretic starred sections (∗) are self-contained and can be included or omitted without loss of continuity.
Structure
The course runs in four parts across fourteen chapters. The alignment convention is strict: Chapter n = Week n = Laboratory Module n = Instructor’s Manual Chapter n, and the Learning Outcome Statements LOS n.k are identical across all four components.
Part I · Uncertainty, Information, and Value (Weeks 1–5)
State prices and the fundamental theorems; probability and financial states; information and filtrations; no-arbitrage valuation; martingales and risk-neutral pricing.
Part II · Dynamics in Continuous Time (Weeks 6–8)
Stochastic processes and Brownian motion; the Itô calculus; derivatives, PDEs, and the Feynman–Kac bridge.
Part III · Optimization, Control, and Learning (Weeks 9–12)
Portfolio choice; stochastic control and the HJB equation; optimal stopping and real options; filtering and hidden states.
Part IV · Risk, Robustness, and Equilibrium (Weeks 13–14)
Coherent risk measures, ambiguity, and robustness; equilibrium, liquidity, and the allocation of capital.
The companion laboratory
Every chapter is backed by three companion artifacts driven by a single seeded Python engine:
- a Laboratory webapp module — interactive, with the book’s validation checks built in;
- a Python notebook — the same computations in code;
- an Excel workbook — one tab per experiment, live formulas beside the engine’s reference values.
All three consume the book’s seeds (2026CCNN, chapter · panel), so their numbers agree by construction. See Labs & Downloads.
Assessment
| Component | Weight |
|---|---|
| Weekly problem sets (Parts A–D) | 40% |
| Laboratory reports (Part E, with validation checks) | 25% |
| Midterm examination (Parts I–II) | 15% |
| Final examination (Parts III–IV) | 20% |
Every laboratory report must reproduce the module’s validation checks; a report whose checks do not pass is returned ungraded. This mirrors professional practice, where a number that cannot be audited is not a number.
Academic integrity
Collaboration on problem sets is encouraged; submitted work must be written individually. Laboratory code may be shared only through the course’s seeded engine, so that reproducibility — not copying — is what the validation checks confirm.