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The sources of sovereign risk: a calibration based on Levy stochastic processes

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The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a sig ...

TAYLOR & FRANCIS LTD2022

Brownian half-plane excursion and critical Liouville quantum gravity

Juhan Aru, Xin Sun

In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be obtained by gluing together a pair of Brownian motions. In this paper, we study the coun ...

WILEY2022

This thesis examines how banks choose their optimal capital structure and cash reserves in the presence of regulatory measures. The first chapter, titled Bank Capital Structure and Tail Risk, presents a bank capital structure model in which bank assets a ...

EPFL2021

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

SPRINGER/PLENUM PUBLISHERS2020

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

This thesis develops three models that study the motivation of various agents to take on debt, and the impact that excessive financial leverage can have on social welfare. In the chapter "Short-term Bank Leverage and the Value of Liquid Reserves", the ince ...

EPFL2019

Linear credit risk models

Damir Filipovic, Damien Edouard Ackerer

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS ...

2019

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Pierre Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

SPRINGER/PLENUM PUBLISHERS2019

Extremal behaviour of aggregated data with an application to downscaling

Sebastian Engelke, Raphaël Gérard Théodore Michel Marie de Deloÿe et Fourcade de Fondeville

The distribution of spatially aggregated data from a stochastic process may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals we introduce the -extremal coefficient, which quantifies this ...

OXFORD UNIV PRESS2019

Polynomial models in finance

Damien Edouard Ackerer

This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for w ...

EPFL2017