A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...
From Plato’s search for hidden forms to Bernoulli’s law of large numbers and Markov’s breakthrough on dependent events, this story traces how mathematicians discovered the patterns hidden inside ...
The probability distribution of the number of defaults plays an important role in pricing problems of multiple-name credit derivatives. When the group size gets large, it becomes increasingly ...