Conner DiPaolo's Blog
Posts
- Identifying Arbitrage Opportunities Across the Whole Options Chain via Linear Programming. We illustrate a method to determine if a no-risk arbitrage opportunity exists across an arbitrary collection of derivatives depending on a single underlying asset. September 2020. [Read More]
- Preprocessing Necessary for Fast, Accurate \(\mathsf{MIPS}\). Recent work on the Maximum Inner Product Search problem in \(d\) dimensions has shown that a \(d\epsilon\)-additive error solution is achievable in sublinear time with no preprocessing. This post shows that a reasonably accurate solution, namely one with \(\epsilon\)-relative error, is unachievable in sublinear time without the use of preprocessing. August 2019. [Read More]
- Investigating \(\boldsymbol{A}_r \otimes \cdots \otimes \boldsymbol{A}_1\) in \(\mathcal{O}(n\log n)\) Time. We show how one can multiply by and solve systems in an \(n\)-dimensional matrix of the form \(\boldsymbol{A}_r \otimes \cdots \otimes \boldsymbol{A}_1\) extremely quickly. In particular, when all \(\boldsymbol{A}_i\) have the same size, both of these operations can be computed in \(\mathcal{O}(n \log n)\) time. July 2019. [Read More]
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