Related papers: Construction of multi-default models with full via…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and…
This paper considers mutual obligations in the interconnected bank system and analyzes their influence on joint and marginal survival probabilities as well as CDS and FTD prices for the individual banks. To make the role of mutual…
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…
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…
We prove the existence of quasi-left continuous semimartingales with continuous local semimartingale characteristics which satisfy a Lyapunov-type or a linear growth condition, where latter takes the whole history of the paths into…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as…
We consider the so-called $\natural$-model. It is an one-default model which gives the conditional law of a random time with respect to a reference filtration. This model has been studied in the case where the parameters are continuous. In…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We study non-linear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and p default martingales. The driver of the BSDE with multiple default jumps can take a generalized form involving an optional finite…
For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…
Given a martingale sequence of random fields that satisfies a natural assumption of boundedness, it is shown that the pointwise limit of this sequence can be modified in such a way that a certain class of moduli of continuity is preserved.…
We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected…
Based on the multidimensional irreducible paving of De March & Touzi, we provide a multi-dimensional version of the quasi sure duality for the martingale optimal transport problem, thus extending the result of Beiglb\"ock, Nutz & Touzi.…
The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of…
The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions of the existence of maximum…
Conic martingales refer to Brownian martingales evolving between bounds. Among other potential applications, they have been suggested for the sake of modeling conditional survival probabilities under partial information, as usual in…