Shiqi Song

Counterparty risk and funding: immersion and beyond

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.

Admissible vectors and their associated Dirichlet forms

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]).

Martingale representation processes and applications in the market viability under information flow expansion

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}.

An enlargement of filtration formula with applications to multiple non-ordered default times

In this work, for a reference filtration F

On arbitrages arising with honest times

\mathbb {F}

An explicit model of default time with given survival probability

, we develop a method for computing the semimartingale decomposition of F

Martingale representation property in progressively enlarged filtrations

\mathbb {F}

Random times with given survival probability and their F-martingale decomposition formula

-martingales in a specific type of enlargement of F

BSDEs of Counterparty Risk

\mathbb {F}

Counterparty Risk Modeling: Beyond Immersion

. As an application, we study the progressive enlargement of F