Notes on some stuff I did and might be of interest to others.
There has been a lot interest on simulation the devolpment of infectious deseases since the COVID-19
pandemic of 2019/20. Many different models and approaches exist to computationally simulate the
spread of infectious deseases.
Using published results for the performance of state-of-the-art AI
document-vector embeddings and semantic hashing I evaluated a canonical
document-vector retrieval system boosted by approximate nearest neighbour
"Erkenntnis macht frei, Bildung fesselt, Halbbildung stürzt in Sklaverei." - Wilhelm Raabe
The cosine measure is the prevailing similarity function for the document vector model of IR. We discuss a its
connection to the intrinsic dimension.
How many servers does Google need for it's web search? How many pages
are crawled and indexed? Starting from Google's 2009 statement that it
uses 1 kJ energy per search we estimate that Google used $\approx$
130.000 servers for its search in 2008. We also speculate that Google
only indexes 5% of its crawled pages.
Hierarchical agglomerative clustering (HAC) is a family of different
algorithms to perform grouping of data. HAC starts by merging the two
data points with smallest distance into a new cluster and finishes with
one big cluster describing the data.
How many pages does Microsoft's search engine Bing.com hold in its index?
Following the idea of Maurice de Kunder
we can roughly estimate the size of Bing's index being 300 million pages.
Initialization of k-means can have a big impact on the performance of the
algorithm. Straight forward random initialization can lead to many more
iterations compared to a better initialization using kmeans++.
Here I show how to price a simple GMDB (unit linked
insurance product) using installment options
and calculate the premium using a binominal tree approach. The
analysis shows that non-rational policy holder behaviour leads
to strong mispricing.
In the previous article
we showed how to price an option using
valuation principle. Following this principle the
arbitrage-free option price is the expected payoff discounted by the
risk-free interest rate. What we were missing until now is how to
calculate the risk-neutral propability $p$.
In this part we will continue our one time-step two states binomial tree
model for pricing an option (previous post
which will leed us to the principle of risk-neutral
The binomial options pricing model provides a numerical method for
the valuation of options. Here I will give a short introduction to
option pricing using the binomial tree model proposed by Cox, Ross
and Rubinstein in 1979 (1)