Initial algebra for a system of right-linear functors

In 2003 we showed that right-linear systems of equations over regular expressions, when interpreted in a category of trees, have a solution when ever they enjoy a specific property that we called hierarchicity and that is instrumental to avoid critical mutual recursive definitions. In this note, we prove that a right-linear system of polynomial endofunctors on a cocartesian monoidal closed category which enjoys parameterized left list arithmeticity, has an initial algebra, provided it satisfies a property similar to hierarchicity

A doctrinal approach to modal/temporal Heyting logic and non-determinism in processes

The study of algebraic modelling of labelled non-deterministic concurrent processes leads us to consider a category LB , obtained from a complete meet-semilattice B and from B-valued equivalence relations. We prove that, if B has enough properties, then LB presents a two-fold internal logical structure, induced by two doctrines definable on it: one related to its families of subobjects and one to its families of regular subobjects. The first doctrine is Heyting and makes LB a Heyting category, the second one is Boolean. We will see that the difference between these two logical structures, namely the different behaviour of the negation operator, can be interpreted in terms of a distinction between non-deterministic and deterministic behaviours of agents able to perform computations in the context of the same process. Moreover, the sorted first-order logic naturally associated with LB can be extended to a modal/temporal logic, again using the doctrinal setting. Relations are also drawn to other computational model

Tribute to Judge Duffy | Kevin Thomas Duffy: I Never Called Him Kevin . . .

Where to begin . . . Clerking for KTD was my first job after graduating from Fordham Law. I was a kid in the law working with a tenured professor who was also the chair of the department. The first lesson was that you worked with KTD. While many of my fellow graduates who were working as clerks were working for a particular judge, I didn’t work for KTD, as he was quick to remind me, I worked with him. It was a collaboration. While I knew nothing really, he insisted we worked as a team. That was the first lesson and one I never forgot. The second lesson quickly on the heels of the first was: No bullshit! If you thought he was going to step in it, you said it out loud. No subtle hints, no multiple cushion shots as in a game of billiards. Just say it out loud. A tough lesson for a very green lawyer, but one he insisted on. He wasn’t offended by my mistakes but he embraced them with a sense of humor, and had a knack to turn them into a lesson in the funniest and most humane way. I always walked away with a smile, never feeling small in the presence of a legal giant. That was an art, a gift he gave to generations of clerks

La copertura del rischio di credito attraverso l'utilizzo dei credit default swap

Nel primo capitolo, dopo un primo approccio al concetto di rischio e alle unità all’interno della banca addette alla sua gestione, è stata data una definizione del rischio bancario analizzando ogni singola fattispecie, ponendo un’attenzione particolare al rischio di credito. Quest’ultimo, figura come il più importante e critico rischio nell’ambito del business bancario in quanto la sua probabilità di insolvenza, insieme alla perdita e alla probabilità di esposizione, costituiscono le misure delle importanti misure di rischio e, di conseguenza, il loro innalzamento corrisponde una crescita nell’applicazione del prezzo dei derivati. Il secondo capitolo analizza la struttura e le peculiarità contrattuali del credit default swap, nel corso del quale, si è posta anche un’attenzione particolare su alcuni modelli matematici utili ai fini della valutazione. Infine, nell’ultimo capitolo, è stato osservato il comportamento operativo di un sovereign CDS e, partendo dal modello CreditMetrics ed alcune assunzioni di base, si è giunti ad una sua valutazione in diversi nei diversi scenari ipotizzati