April 25, 2024
A derivative security is a contract: I will give you this on these dates if you will give me that on those dates. The ‘I’ and ‘you’ are legal entities. One of them is buying the contract and the other is selling. The hallmark of a derivative security is the dates, ‘this’, and ‘that’ can depend on what happens in the future.
An exchange… has price …
Determined up to isomorphism by dimension.
Linear transformation.
Matrix multiplication is composition of linear transformations.
Dual space.
Adjoint.
\mathbf{R}^n, e_j
T\colon\mathbf{R}^n \to V, (a_j)\mapsto \sum_j a_j v_j.
Independent: injective
Span: surjective
Basis: bijective
e^j.
norm, inner product
Random variable X\colon\Omega\to\mathbf{R}.
Measure B(\Omega)^* = ba(\Omega).
Students want to acquire knowledge that will help them get a job and be successful.
Our job is to streamline presentation of state-of-the-art knowledge to students.
The state of the art is rapidly changing so it is important to develop relationships with companies to understand what they are looking for. We no longer have Peter who knows everyone. It would be no surprise if you already have a list of companies and who makes their hiring decisions. It is important to keep that up-to-date and to reach out on a regular basis. They have quants that would jump at the chance to give a talk at NYU. Peter was a natural at getting people to communicate. The rest of us have to make an effort.