diff --git a/README.md b/README.md index 0269bf8..7955f89 100644 --- a/README.md +++ b/README.md @@ -26,18 +26,15 @@ pip install --upgrade pip Quant DSL is domain specific language for quantitative analytics in finance and trading. -At the heart of Quant DSL is a set of elements (e.g. `Settlement`, `Fixing`, `Market`, `Wait`, -`Choice`) which encapsulate maths used in finance and trading. The elements of the language can -be freely composed into expressions of value. - +At the heart of Quant DSL is a set of elements (e.g. "Settlement", "Fixing", "Market", "Choice"). The elements involve mathematical expressions commonly used within quantitative analytics, such as: -[present value discounting](https://en.wikipedia.org/wiki/Present_value) for the `Settlement` element; -[geometric Brownian motion](https://en.wikipedia.org/wiki/Geometric_Brownian_motion) for the `Market` element; and -[least squares Monte Carlo](https://en.wikipedia.org/wiki/Monte_Carlo_methods_for_option_pricing#Least_Square_Monte_Carlo) -for the `Choice` element. +[present value discounting](https://en.wikipedia.org/wiki/Present_value); +[geometric Brownian motion](https://en.wikipedia.org/wiki/Geometric_Brownian_motion); and +[least squares Monte Carlo](https://en.wikipedia.org/wiki/Monte_Carlo_methods_for_option_pricing#Least_Square_Monte_Carlo). -The validity of Monte Carlo simulation for all possible expressions in the language is +The elements of the language can be freely composed into expressions of value. The validity of +Monte Carlo simulation for all possible expressions in the language is [proven by induction](http://www.appropriatesoftware.org/quant/docs/quant-dsl-definition-and-proof.pdf). @@ -63,8 +60,9 @@ The syntax of Quant DSL expressions is defined with ### Semantics -Quant DSL expression `v` defines a function `[[v]](t)` from present time `t` to a random -variable in a probability space. +In the definitions below, Quant DSL expression `v` defines a +function `[[v]](t)` from present time `t` to a random +variable in a probability space. ``` @@ -151,6 +149,7 @@ are discarded as soon as they are no longer required, such that memory usage is evaluation. For the delta calculations, nodes are selectively re-evaluated with perturbed values, according to the periods and markets they involve. + ### calc() The examples below use the library function `calc()` to evaluate Quant DSL source code. It uses the methods of the