Asset prices discounted by a tradable numeraire N should be (local) martingales under some measure Q that is equivalent to the original probability measure P. Instead of studying the set of equivalent martingale measures with respect to a prespecified numeraire, we will look for a tradable...

We solve the superhedging problem for European options in an illiquid extension of the Black–Scholes model, in which transactions have transient price impact and the costs and strategies for hedging are affected by physical or cash settlement requirements at maturity. Our analysis is based on...

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>

Let $X$ be a special semimartingale of the form $X=X_0+M+\int d\langle M\rangle\,\widehat\lambda$ and denote by $\widehat K=\int \widehat\lambda^{\rm tr}\,d\langle M\rangle\,\widehat\lambda$ the mean-variance tradeoff process of $X$. Let $\Theta$ be the space of predictable processes $\theta$...

An implied savings account for a given term structure model is a strictly positive predictable process A of finite variation such that zero coupon bond prices are given by $B(t,T)=E^Q\left[{A_t \over A_T} \Big| {\cal F}_t \right]$ for some Q equivalent to the original probability measure. We...