We provide a concise exposition of theoretical results that appear in modeling default time as a random time, we study in details the invariance martingale property and we establish a representation theorem which leads, in a complete market setting, to the hedging portfolio of a vulnerable...

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time τ gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit...

Let $X$ be an ${\Bbb R}^d$-valued special semimartingale on a probability space $(\Omega , {\cal F} , ({\cal F} _t)_{0 \leq t \leq T} ,P)$ with canonical decomposition $X=X_0+M+A$. Denote by $G_T(\Theta )$ the space of all random variables $(\theta \cdot X)_T$, where $\theta $ is a predictable...

As a corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463–520, <CitationRef CitationID="CR5">1994</CitationRef>; Stoch. Stoch. Rep. 53:213–226, <CitationRef CitationID="CR6">1995</CitationRef>; Math. Ann. 312:215–250, <CitationRef CitationID="CR7">1998</CitationRef>), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit...</citationref></citationref></citationref>