Analytical and numerical approach to corporate operational risk modelling

Although The New Basel Accord gives the methodology for managing operational risk in financial institutions, corporate risk seems not to be recognized enough. In this Ph.D. thesis we make an attempt to put some insight into operational risk measurement in a non-financial corporation. The objective is to apply suitable results from insurance ruin theory to build a framework for measuring corporate operational risk and finding required capital charge.Corporate risk management; Operational risk; Actuarial risk theory; Ruin probability; Operational reserves;

Moments of polynomial functionals in Levy-driven queues with secondary jumps

A long-standing open problem concerns the calculation of the moments of the area beneath the M/G/1 workload graph during a busy period. While expressions for the first two moments were known, no results for higher moments were available. This paper includes a recursive algorithm to compute all moments in terms of the model primitives. Our results extend to any storage system fed by a superposition of a drifted Brownian motion and a subordinator with a secondary jump input, yielding the moments of a general class of polynomial functionals of the workload process. Some applications of these moments are also provided

On the area between a L\'evy process with secondary jump inputs and its reflected version

We study the the stochastic properties of the area under some function of the difference between (i) a spectrally positive L\'evy process $W_t^x$ that jumps to a level $x>0$ whenever it hits zero, and (ii) its reflected version $W_t$. Remarkably, even though the analysis of each of these processes is challenging, we succeed in attaining explicit expressions for their difference. The main result concerns the Laplace-Stieltjes transform of the integral $A_x$ of (a function of) the distance between $W_t^x$ and $W_t$ until $W_t^x$ hits zero. This result is extended in a number of directions, including the area between $A_x$ and $A_y$ and a Gaussian limit theorem. We conclude the paper with an inventory problem for which our results are particularly useful