Inter-Temporal Choice
Last edited: August 8, 2025Goal
We are going to solve the inter-temporal choice problem, for ten time stamps, and perform some numerical optimization of the results
Main Methods
We do this by solving backwards. We will create a variable \(k\) to measure asset, and \(k_{t}\) the remaining asset at time \(t\).
Let us first declare the function for power utility. \(k\) is our asset holding, \(\gamma\) our relative margin of risk, and \(U\) the power utility.
Interaction Uncertainty
Last edited: August 8, 2025The interaction of multiple agents/decision makers causes additional uncertainty
Interactive Proof
Last edited: August 8, 2025We have prover \(P\) and randomized verifier \(V\). The \(V\) asks \(P\) for membership statements, and \(P\) responds with statements. These proofs can be used to prove membership in very powerful languages.
Languages \(L\) with a \(k\) round interactive proof system, where the verifier \(V\) is poly randomized machine and its interacting with an all-powerful prover \(P\).
- \(x \in L \implies \exists_{ \text{prover}}\) such that \(V\qty(x_1, \dots, y_{k})\) accepts with probability \(\geq \frac{2}{3}\)
- \(x \not \in L \implies \forall _{\text{prover}}\) such that \(V\qty(x_1, \dots, y_{k})\) accepts with probability \(\leq \frac{1}{3}\)
interpolation
Last edited: August 8, 2025nyquist limit is great and all, but I really don’t want to wait for all \(T\) to be able to sample all the necessary terms to solve for every \(a_{j},b_{j}\) before we can reconstruct our signal.
So, even if we got our sequence of \(\frac{1}{2B}\) length of points, we need an alternative way to reconstruct the signal as we go.
One way to reconstruction via interpolation is just to connect the dots; however, this is bad because it creates sharp corners.