Shiqi Song
Université Paris-Saclay
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Featured researches published by Shiqi Song.
Finance and Stochastics | 2016
Stéphane Crépey; Shiqi Song
In Crépey (Math. Finance 25:23–50, 2015), a basic reduced-form counterparty risk modelling approach was introduced under a standard immersion hypothesis between a reference filtration and the filtration progressively enlarged by the default times of the two parties. This basic setup, with a related continuity assumption on some of the data at the first default time of the two parties, is too restrictive for wrong-way and gap risk applications, such as counterparty risk on credit derivatives. This paper introduces an extension of the basic approach, implements it through marked default times and applies it to counterparty risk on credit derivatives.
Potential Analysis | 1992
Shiqi Song
Bouleau and Hirsch have introduced in [4] the energy-image density property and have proved that such property held for the Dirichlet form associated with the classical Wiener space. We will extend their result by proving that such energy-image density property holds more generally for the classical Dirichlet forms (see [1] for the terminology) on any infinite dimensional topological vector spaces provided with admissibility (introduced by Albeverio-Röckner in [1]).
Esaim: Proceedings | 2017
Shiqi Song; Stéphane Crépey; Monique Jeanblanc; Ashkan Nikeghbali
When the \textit{martingale representation property} holds, we call any local martingale which realizes the representation a \textit{representation process}. There are two properties of the \textit{representation process} which can greatly facilitate the computations under the \textit{martingale representation property}. Actually, on the one hand, the \textit{representation process} is not unique and there always exists a \textit{representation process} which is locally bounded and has pathwisely orthogonal components outside of a predictable thin set. On the other hand, the jump measure of a \textit{representation process} satisfies the \textit{finite predictable constraint}. In this paper, we give a detailed account of these two properties. As application, we will prove that, under the \textit{martingale representation property}, the \textit{full viability} of an expansion of market information flow implies the \textit{drift multiplier assumption}.
Finance and Stochastics | 2018
Monique Jeanblanc; Libo Li; Shiqi Song
In this work, for a reference filtration F
Finance and Stochastics | 2014
Claudio Fontana; Monique Jeanblanc; Shiqi Song
\mathbb {F}
Stochastic Processes and their Applications | 2011
Monique Jeanblanc; Shiqi Song
, we develop a method for computing the semimartingale decomposition of F
Stochastic Processes and their Applications | 2015
Monique Jeanblanc; Shiqi Song
\mathbb {F}
Stochastic Processes and their Applications | 2011
Monique Jeanblanc; Shiqi Song
-martingales in a specific type of enlargement of F
Stochastic Processes and their Applications | 2015
Stéphane Crépey; Shiqi Song
\mathbb {F}
Archive | 2014
Stéphane Crépey; Shiqi Song
. As an application, we study the progressive enlargement of F