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Xin He

Bio: Xin He is an academic researcher from Beijing Normal University. The author has contributed to research in topics: Branching process & Jump. The author has an hindex of 1, co-authored 1 publications receiving 15 citations.

Papers
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Journal ArticleDOI
TL;DR: A representation is given for the distribution of the first jump time of the process with jump size in a given Borel set and the equivalence of this distribution and the total Lévy measure is studied.
Abstract: We study the distributional properties of jumps in a continuous-state branching process with immigration. In particular, a representation is given for the distribution of the first jump time of the process with jump size in a given Borel set. From this result we derive a characterization for the distribution of the local maximal jump of the process. The equivalence of this distribution and the total Levy measure is then studied. For the continuous-state branching process without immigration, we also study similar problems for its global maximal jump.

19 citations


Cited by
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01 Jan 2016
TL;DR: This introduction to stochastic calculus applied to finance will help people to understand better how to deal with malicious downloads and how to protect themselves from malicious downloads.
Abstract: Thank you very much for reading introduction to stochastic calculus applied to finance. Maybe you have knowledge that, people have search numerous times for their favorite readings like this introduction to stochastic calculus applied to finance, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they are facing with some malicious virus inside their laptop.

82 citations

Book ChapterDOI
TL;DR: In this paper, a brief introduction to continuous-state branching processes with or without immigration is given, where the processes are constructed by taking rescaling limits of classical discrete state branching models and given characterizations of the local and global maximal jumps of the processes.
Abstract: This work provides a brief introduction to continuous-state branching processes with or without immigration. The processes are constructed by taking rescaling limits of classical discrete-state branching models. We give quick developments of the martingale problems and stochastic equations of the continuous-state processes. The proofs here are more elementary than those appearing in the literature before. We have made them readable without requiring too much preliminary knowledge on branching processes and stochastic analysis. Using the stochastic equations, we give characterizations of the local and global maximal jumps of the processes. Under suitable conditions, their strong Feller property and exponential ergodicity are studied by a coupling method based on one of the stochastic equations.

43 citations

Journal ArticleDOI
TL;DR: A market model for power prices is investigated, including most basic features exhibited by previous models and taking into account self-exciting properties, and a Random Field approach is proposed, extending Hawkes-type models by introducing a twofold integral representation property.

34 citations

Journal ArticleDOI
TL;DR: The α-CIR model as mentioned in this paper is an extension of the standard CIR model by adopting the α-stable Levy process and preserving the branching property, which allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market together with the presence of large jumps at local extent.
Abstract: We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable Levy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations.

33 citations

Journal ArticleDOI
TL;DR: In this paper, an affine extension of the Heston model is introduced where the instantaneous variance process contains a jump part driven by α-stable processes with α ∆ in(1,2]$ in(α ∆)-stable processes.
Abstract: We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by $\alpha$-stable processes with $\alpha\in(1,2]$ In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options Furthermore, we examine the jump clustering phenomenon observed on the variance market and provide a jump cluster decomposition which allows to analyse the cluster processes

19 citations