Some time ago I used a time series forecasting approach based on time inversion beautifully incorporated in a special type of recurrent neural network invented by Dr. Hans-Georg Zimmermann — a world-class deep learning practitioner who led a research of neural networks in application to the industrial & financial problems at Siemens for many years [1]. The underlying philosophical ideas he utilized lie beyond the scope of Christopher Nolan’s TENET, but still, the approach remains super legit.

The Idea of TENET

A dynamical system is a group of related things which state changes over time. Open systems can react to an environment, while closed…

Game theory studies rational agents’ interactions in various environmental settings. Many business problems can be formulated in a game theory fashion, but in order to be able to study them, researches have to narrow the real world complexity by 1) limiting the freedom of agents’ actions and 2) omitting many long-term and second-order effects originating from the environment. Due to the simplification often models obtained are hardly applicable to real life business problems. Otherwise we would have already lived in the world of highly efficient markets where all decisions are made by computers.

Despite that the assumption of agents’ rationality…

When you conduct a bottom-up analysis of a business with customers there is one metric you definitely need to know — Customer Lifetime Value (LTV), i.e. how much profit a customer brings in over a whole period of economic relationship.

LTV is a very popular topic of business discussion and you will find a lot of different formulas to calculate it if you google it, but I will dive into plain mathematical aspect of this concept, which is not so well represented over the internet.

Consider a subscription based service (e.g. Netflix) where a customer pays at the end of…