Works in progress on mathematics. Please contact me if you have questions, comments, or suggestions.
| Name | Description |
| 123 | Not as easy as 1, 2, 3. |
| a | |
| a_z | How to structure a mathematical argument. |
| apl | A Programming Language |
| bach | Normal stock price |
| basic | Basic model. |
| bayes | Conditional probability |
| bigo | Back of the envelope calculations. |
| bio | |
| blurb | |
| bm | Continuous time random walk |
| bonds | Terminology for bonds |
| bqn | Category Theory for Array Languages |
| bsm | Valuation formula. |
| capm | Two assets suffice for optimal portfolios. |
| cat | Objects and Arrows |
| cdf | Facts about cumulative distribution functions |
| ce | Probability given information |
| cm | Payoffs can be replicated with cash, a forward, and a portfolio of puts, and calls |
| copula | A copula is a probability measure on unit cubes. |
| coro | Coroutines are functions and a continuation point. |
| curry | Relationship between Cartesian product and exponentials. |
| db | The mathematical foundations of databases. |
| de | |
| det | Hermann Grassmann showed us how. |
| div | Dividend paying stock |
| dual | Mirror, mirror, ... |
| ec | They're, like, totally modular dude. |
| ecr | Computation is the composition of relations |
| eebo | Sometimes you need math. |
| eli5 | |
| ep | The Capital Asset Pricing Model holds as equality of random variables, not just their expected values. |
| ep_cover | |
| ep_title | | |
| eps | |
| eth | Crypto is not cryptic |
| factors | Are 1-factor models |
| falg | Category with structure |
| fc | Apply a function to a linear transformation |
| fd | Infinite dimensional derivatives |
| ff | Evincing the real world in Mathematical Finance |
| fi | Fixed cash flows |
| fin | |
| fof | Entity, instrument, price, cash flow, trading, value, account |
| fsa | |
| funny | Path dependent volatility. |
| ga | The algebra of space |
| gla | Linear algebra is a special case of Geometric Algebra |
| gop | European option pricing and greeks |
| ho-lee | Normal short rate. |
| ice | |
| int | Integration is a linear functional on a vector space of functions. |
| ip | Brownian motion and the heat equation. |
| is | Do they exist? |
| ito | Stochastic differential equations and integrals |
| kal | |
| kh | Remarks on [Carabelli](https://www.researchgate.net/publication/263531626_Further_issues_on_the_Keynes-Hume_connection_relating_to_the_theory_of_financial_markets_in_the_General_Theory/link/02e7e53c9697895f81000000/download) |
| la | A guide to Linear Algebra. |
| lagd | Linear Algebra from the Ground Down |
| lambda | The lambda calculus |
| lfc | none |
| lo | The foundation of mathematics. |
| mcmc | |
| measure | Do not count twice |
| mf | Key topics. |
| mfm | Work remains to be done. |
| ml | Interpolation in high dimensions |
| mo | Associative binary operation with an identity |
| monad | Will it Function? |
| njr | Perturbation of the normal distribution |
| ode | Ordinary Differential Equations |
| op | European option pricing and greeks |
| op2 | European option pricing and greeks |
| opm | Buy now, sell later. |
| opm2 | Buy now, sell later. |
| optics | Lenses, Prisms, Grates, and Traversals |
| pc | |
| pcp | |
| pdv | Volatility is path dependent. |
| pes | Writing performant code that can be used from any language |
| pnl | P&L is stochastic integration. |
| pq | |
| prob | A calculus for uncertainty |
| profile | |
| ps | Writing performant code that can be used from any language |
| pt | The mathematical foundations of pivot tables. |
| raii | Worst name ever for built-in types. |
| rel | Relation – comparing two things. |
| remf | |
| res | |
| rl | | |
| ro | Value, hedge, and manage risk of any portfolio |
| rw | Move based on coin flip |
| set | Sets are defined by membership |
| sf | More power to the functions |
| shimko | |
| simfin | |
| simple | | |
| sofr | Short Rates |
| sofrsg | One more thing to figure out. |
| sp | Random variables indexed by time |
| stat | Observations of outcomes |
| tilfp | |
| tim | A _monad_ is a _monoid_ on the _endofunctors_ of a _category_. |
| tlh | Tax loss harvesting |
| tmt | The dominance of unimportance. |
| tnbt | |
| tos | Totally ordered streams. |
| tpm | Examples |
| trading | Buyers and sellers buy and sell |
| ts | Primative operations |
| u | Value, hedge, and manage risk of any portfolio |
| uf | Unified Finance – positions, portfolios, exchanges, and trading |
| um | Value, hedge, and manage risk of any portfolio |
| um0 | Value, hedge, and manage the risk of any instruments |
| um1 | Value, hedge, and manage the risk of instruments |
| um2 | Value, hedge, and manage the risk of any instruments |
| um_short | Value, hedge, and manage risk of any portfolio |
| um_slides | |
| umm | Value, hedge, and manage risk of any portfolio |
| ums | |
| vs | For European options |
| vs0 | Abelian group with scalar multiplication satisfying the distributed law. |
| vswap | Value, hedge, and manage risk of variance swaps. |
| wc | |
| wif | Atoms of finance and their interaction. |
| wmpl | It is not just bean counting. |
| wtd | How to value, hedge, and manage risk |
| ycm | Continuously compounded stochastic forward rate |
| yo | Work remains to be done. |
| zcb | Moving unit notional through time. |