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An optimal prediction problem in financial modelling

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Numerical methods for option pricing: polynomial approximation and high dimensionality

Francesco Statti

Options are some of the most traded financial instruments and computing their price is a central task in financial mathematics and in practice. Consequently, the development of numerical algorithms for pricing options is an active field of research. In gen ...

EPFL2019

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

Sylvain Jean Pascal Carré, Daniel Cohen

Governments choose to issue risky or riskless debt depending on the nature of the stochastic process of output. We use Brownian motion and Poisson shocks a modeling method in the literature on corporate default known as Levy processes to approximate a deco ...

ELSEVIER SCIENCE BV2019

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

Financial Stability and the Macroeconomy

Corinne Dubois

The financial crisis of 2007-2009 drew attention to the essential role of banks for the macroeconomy and to the importance of having a resilient financial sector. A vulnerability in the financial sector spills over to the real economy and can drive it into ...

EPFL2018

Investment Dynamics with Natural Expectations

Andreas Fuster

We study an investment model in which agents have the wrong beliefs about the dynamic properties of fundamentals. Specifically, we assume that agents underestimate the rate of mean reversion. The model exhibits the following six properties: (i) Beliefs are ...

2018

Optimal Financial Decision Making Under Uncertainty

Daniel Kuhn

We use a fairly general framework to analyze a rich variety of financial optimization models presented in the literature, with emphasis on contributions included in this volume and a related special issue of OR Spectrum. We do not aim at providing readers ...

Springer International Publishing2017

Generalized Pickands constants and stationary max-stable processes

Sebastian Engelke

Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, D ...

Springer Verlag2017

Solving Stochastic AC Power Flow via Polynomial Chaos Expansion

Timm Faulwasser

The present contribution demonstrates the applicability of polynomial chaos expansion to stochastic (optimal) AC power flow problems that arise in the operation of power grids. For rectangular power flow, polynomial chaos expansion together with Galerkin p ...

IEEE2016

A Levy-derived process seen from its supremum and max-stable processes

Sebastian Engelke

We consider a process Z on the real line composed from a Levy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of the supremum (Z) over bar, its time T, and the process Z(T + center dot) - (Z ...

Univ Washington, Dept Mathematics2016