MFMF LaboratoryiInteractive companion to Mathematical Foundations of Modern Finance. Every result is seeded and matches the book's notebook and workbook.

Mathematical Foundations of Modern Finance
UncertaintyiThe set of possible future states before any information arrives — the raw material of every model.·
InformationiA filtration Fₜ — what you can distinguish at date t; conditions every expectation and decision.·
ValueiA linear pricing functional on payoffs. State prices ψ, the risk-neutral measure Q, and the SDF m are three languages for it.·
TimeiDiscrete- or continuous-time dynamics: horizons, rebalancing frequency, quadratic variation.·
DecisioniThe choice variable: portfolio weights, consumption rate, exercise policy — solved via Bellman/HJB.·
RiskiHow losses aggregate across scenarios: VaR, expected shortfall, coherent risk measures.·
AggregationiPrices as market clearing across heterogeneous agents — the equilibrium that closes the system.
Where you are in the system.
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iServer-side reproducibility checks for this chapter. Green means every book number reproduces exactly.
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Chapter 1

Mathematical Architecture & the SandboxiThe one-period binomial market. Introduces state prices, the risk-neutral measure, and the SDF as three languages for the same price.

iOne-period binomial market: price a European call by state prices and by the risk-neutral measure, then check they agree to the cent.
iSweep the gross rate R. The alarm fires when R leaves the (d, u) no-arbitrage band and an arbitrage appears.
iCompare the physical (P) and risk-neutral (Q) probabilities and see why discounting the physical mean gives the wrong price.
iAdd a third state the two assets cannot span — the single price becomes an interval.

A one-period, two-state market: the index moves up or down; a bond grows at the gross rate R. Price the European call.iOne-period binomial market: price a European call by state prices and by the risk-neutral measure, then check they agree to the cent.