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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...