arXiv subjects

Vivien Brunel

Publications and source records attributed to Vivien Brunel.

3 recordsLinked to original sources

arXiv2017

A general asymptotic formula for distinct partitions

Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is valid for any value of the number of parts. We obtain general asymptotic formulas for distinct partitions that are valid in a wider range of parameters than the existing asymptotic formulas, and we recover the known asymptotic results as special cases of our general formulas.

math.CO↗

arXiv2015

Operational risk modeled analytically II: the consequences of classification invariance

Most of the banks' operational risk internal models are based on loss pooling in risk and business line categories. The parameters and outputs of operational risk models are sensitive to the pooling of the data and the choice of the risk classification. In a simple model, we establish the link between the number of risk cells and the model parameters by requiring invariance of the bank's loss distribution upon a change in classification. We provide details on the impact of this requirement on the domain of attraction of the loss distribution, on diversification effects and on cell risk correlations.

q-fin.RM↗

arXiv2014

Analytical models of operational risk and new results on the correlation problem

We propose a portfolio approach for operational risk quantification based on a class of analytical models from which we derive new results on the correlation problem. In particular, we show that uniform correlation is a robust assumption for measuring capital charges in these models.

q-fin.RM↗