Graduate Finance · One Integrated System
Mathematical Foundations of Modern Finance
Graduate finance rebuilt from its mathematical foundations — a single integrated system running from state prices to equilibrium. Every chapter opens with a decision facing the Meridian Endowment investment committee and closes with a hands-on laboratory module. Fourteen chapters, four parts, one continuous argument.
The seven primitives — the spine of the book
01 Uncertainty Ch 2
02 Information Ch 3
03 Value Ch 4–5
04 Time Ch 6–8
05 Decision Ch 9–12
06 Risk Ch 13
07 Aggregation Ch 14
Why this course exists
Modern finance is usually taught as a sequence of disconnected topics: a probability review, then options, then portfolios, then risk, each with its own notation and its own worked examples. This course takes the opposite stance. It treats finance as one integrated system — uncertainty, information, valuation, dynamics, optimization, risk, and equilibrium are seven faces of a single object, and the same state-price mathematics that prices an equity collar in Chapter 4 disciplines the private-asset valuation, the spending rule, the timing decision, and the risk limit in the chapters that follow.
The organizing device is concrete. Every chapter opens with an item from the agenda of the Meridian Endowment investment committee — price and approve a collar, accept a private-asset valuation, rebalance toward policy weights, commit now or wait, ratify a risk limit — and resolves it with exactly the mathematics that item requires. By Chapter 14 the committee’s opening question, where do the prices come from?, is answered with the full toolkit in hand.
The three companions
One engine, three ways to use it
Every laboratory module is backed by a single seeded Python engine. The notebook, the workbook, and the webapp all consume that engine with the book’s seeds, so the numbers agree by construction.
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Laboratory Webapp
Fourteen chapter dashboards implementing every Modern Finance Laboratory module — interactive, seeded, and validated against the book.
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Python Notebooks
One notebook per chapter driving the same engine, with the book’s validation checks built in and ready to run.
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Excel Workbooks
One workbook per chapter, one tab per laboratory experiment — live formulas beside the engine’s reference values.
All three consume the same Python engine with the book’s seeds (2026CCNN, chapter · panel), so the numbers agree by construction.
What you will build
- Fluency in the three languages of valuation — state prices, stochastic discount factors, and risk-neutral expectation — and the discipline to move between them without losing the thread.
- A working command of the book’s core machinery: no-arbitrage and completeness, the Itô calculus and Feynman–Kac, dynamic programming and the HJB equation, optimal stopping, filtering, coherent risk measures, and equilibrium.
- Hands-on competence with the companion laboratory: every chapter has a webapp module, a Python notebook, and an Excel workbook, all producing identical numbers on identical seeds.
- The habit of auditing your own numbers: every laboratory module carries the book’s validation checks, and passing them is part of every assignment.
Chapters
Part I · Uncertainty, Information, and Value
Chapter 1The Mathematical Architecture of Modern FinanceModule 1 · Probability and State Space Explorer Chapter 2Probability, Uncertainty, and Financial StatesModule 2 · Probability and Distribution Lab Chapter 3Information, Conditional Expectation, and FiltrationsModule 3 · Information and Conditional Expectation Simulator Chapter 4Valuation, No-Arbitrage, and State PricesModule 4 · State Prices, Completeness, and Bounds Chapter 5Martingales, Change of Measure, and Risk-Neutral ValuationModule 5 · Fair Games, Measure Change, and Dynamic Hedging
Part II · Dynamics in Continuous Time
Chapter 6Stochastic Processes and Financial DynamicsModule 6 · Paths, Quadratic Variation, and Jumps Chapter 7Itô Calculus and Continuous-Time FinanceModule 7 · Stochastic Calculus in the Hands Chapter 8Derivatives, PDEs, and the Feynman–Kac BridgeModule 8 · The Pricing Machine
Part III · Optimization, Control, and Learning
Chapter 9Portfolio Choice and Dynamic OptimizationModule 9 · The Allocation Laboratory Chapter 10Stochastic Control and the HJB EquationModule 10 · The Control Room Chapter 11Optimal Stopping and Real OptionsModule 11 · The Timing Desk Chapter 12Filtering, Learning, and Hidden StatesModule 12 · The Learning Machine
Part IV · Risk, Robustness, and Equilibrium