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In this paper we introduce a new coherent cumulative risk measure on a subclass in
the space of càdlàg processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy...

The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationa...

The field of risk theory has traditionally focused on ruin-related quantities. In particular, the so-called expected discounted penalty function (Gerber and Shiu. N Am Actuar J, 2(1):48–78, 1998) has been the object of a thorough study over the years. Although interest...

In [12], the concept of natural risk statistics is introduced as a data-based risk measure, i.e. as
an axiomatic risk measure defined in the space Rn. In this note, we set to generalize this notion to
bivariate data sets (more generally, multivariate data sets) by defi...

Regime-switching models (RSM) have been recently used in the literature as alternatives to the Black-Scholes model. Several authors favor RSM as being more realistic since, by construction, they model those exogenous macroeconomic cycles against which asset prices evol...

In this paper we study the ruin problem for an insurance risk process driven by a spectrally-positive Markov additive process. Particular attention is given to the family of spectrally-positive Markov-modulated Lévy processes. We give an expression for the expected dis...

We consider the problem of pricing contingent claims using distortion operators. This approach was first developed in (Wang, 2000) where the original distortion function was defined in terms of the normal distribution. Here, we introduce a new distortion based on the N...

April 2, 2010

 

Axiomatically based risk measures have been the object of numerous studies and generalizations in recent years. In the literature we find two main schools: coherent risk measures (Artzner, Coherent Measures of Risk. Risk Management: Value at Risk and Beyond, 1998) and...

September 11, 2009

The Expected Discounted Penalty Function (EDPF) was introduced in a series of now classical papers. Motivated by applications in option pricing and risk management, and inspired by recent developments in fluctuation theory for Lévy processes, we study an extended defin...

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Simulator Models for the Limit Order Book Dynamics and their Applications

December 3, 2016

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Department of Mathematics and Statistics

University of Montreal

© 2016 by Manuel Morales.

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