Divide-and-Conquer
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The Joint Limit Distribution
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Risk Revealed
Abstract: The title of my talk refers to a forthcoming book, to be published by Cambridge University Press, co-authored with Valérie Chavez-Demoulin (Lausanne) and Marius Hofert (Waterloo/Hong Kong University). Extreme Value Theory (EVT) offers a mathematical tool for the modeling of so-called What-If events, or stress scenarios. I will present several examples of risk-based decision-making […]
Fourier-Z Pricing of Discretely Monitored
Abstract: Several path-dependent options with discrete monitoring like barrier, lookback and alpha-quantile can be priced exploiting fluctuation identities, which provide the z-transform of the characteristic function of the extrema of a L’evy stochastic process, possibly conditional on touching certain levels. A numerical inverse z-transform (IZT) is necessary to retrieve the characteristic function for pricing. Implementing […]
A New Approach to Posson Approximation and Some Refinements
Abstract: In this talk I will introduce the so-called mod-Poisson approximation schemes to obtain asymptotic and non asymptotic results in the context of Poisson approximation for various distances. The results rely on simple facts from the theory of absolutely convergent Fourier series on the torus (the Wiener algebra) and basic facts from the algebra of […]
Relative Frecuency Between Two Continuous State Branching Processes
Abstract: Heuristically, there is a strong relationship between continuous-state branching (CB) processes and coalescents. However, explicitly providing it, is a problem that has a long history. We shall see some known results of this relationship and construct, under certain conditions an explicit homeomorphism between the two families of processes using our previous results on the […]
Markovian Solutions for Scalar Conservation Laws
Abstract: Groeneboom in 1989 discovered an explicit formula for the law of the entropy solution to Burgers’ equation when the initial condition is white noise. The method of his proof relied extensively on probabilistic methods and in particular on the sophisticated excursion theory for diffusions. Recently, by verifying a conjecture of Menon and Srinivasan, Kaspar […]
Levy Processes and self -similar Markov processes
Abstract: In this talk, we will look at the interaction between the theory of self-similar Markov processes and the theory of Lévy processes through the lens of α-stable Lévy processes. In particular, we will explore how the two theories are closely interlaced via a space-time path transformation known as the Lamperti transform. Moreover, as one […]
Quasi-Infinitely divisible distributions
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چين
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