We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining this insight with well known results from J. M\'emin and L....

In the context of large financial markets we formulate the notion of "no asymptotic free lunch with vanishing risk" (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for...

The analytical tractability of affine (short rate) models, such as the Vasi\v{c}ek and the Cox-Ingersoll-Ross models, has made them a popular choice for modelling the dynamics of interest rates. However, in order to account properly for the dynamics of real data, these models need to exhibit...

We obtain a first order extension of the large deviation estimates in the G\"{a}rtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The...

We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point...

We provide a new dynamic approach to scenario generation for the purposes of risk management in the banking industry. We connect ideas from conventional techniques -- like historical and Monte Carlo simulation -- and we come up with a hybrid method that shares the advantages of standard...

We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to obtain applicable formulas for option pricing in pre-computer...

We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in...

We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable...

In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional It\^{o}-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently...