# C# Lists and Dictionary

In C# there are several key differences to C++. Microsoft Website spells them all: https://msdn.microsoft.com/en-us/magazine/cc301520.aspx Garbage collector instead of deconstructors providing a different approach to micromenagment of memory and lists, jagged arrays and dynamic memory allocation are already available into the language. It supports also negative index to counting from the last element, similarly to Python. About lists instead of the usual self-made textbook-example class, there are specific embedded classes for Lists and Dictionaries.

# Fun with conditional probability

Bayesian concept of probability is linked not with frequency, but with state of information. The processing of this information proceeds in a propositional sense. In fact there are semantic work related to the use of Bayesian statistic as foundation for programming languages (BLOG), First kind logic (MEBN , also look at the fun Of Starships and Klingon) and thus the foundation principles of Network-Centric warfare and commerce.

Property of Baysian calculation of proabability are sometimes difficult to grasp and very counter intuitive, interesting consideration can hide behind apparently trivial formulas that can help to answer questions like: If you know your neighbour has a son born on Tuesday, which is the probability your neighbour has two sons?

# Value at Risk on expected return

Value at Risk on expected return is the lower bound for the loss in an investement respect to a probability. Is a way to estimating losses probabilities in terms of value, instead of standard deviation. E.g. in the case of , means that the investor have a probability of loosing € or more, investing € on the portfolio . Considering the system ergodic and thus all the variances of the titles summing up coherently to for a variance of the portfolio distributed within the normal distribution, this is simply calculated considering the quantile (the value of the distribution corresponding to a certain fraction of probability) .

# No-Arbitrage condition

No Arbitrage states the inadmissibility of Free Lunch in applying a structure (metric?) to the prices. Considering a title with price and cash flow , or every time , where it is the discretized time . Then we have the two No-Arbitrage condition: Weak No-Arbitrage : if Strong No-Arbitrage: if and Let’s suppose a world where I can borrow money with fixed interest rate , which will be the price of a product with interest over one year?