Related papers: Construction of multi-default models with full via…
In this note we classify quasi-sum production functions with constant elasticity of production with respect to any factor of production and with proportional marginal rate of substitution.
The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
We discuss the pricing of defaultable assets in an incomplete information model where the default time is given by a first hitting time of an unobservable process. We show that in a fairly general Markov setting, the indicator function of…
We build on the stability-preserving school choice model introduced and studied recently in [MV18]. We settle several of their open problems and we define and solve a couple of new ones.
Given a graph $G$ and collection of subgraphs $T$ (called tiles), we consider covering $G$ with copies of tiles in $T$ so that each vertex $v\in G$ is covered with a predetermined multiplicity. The multinomial tiling model is a natural…
Given the univariate marginals of a real-valued, continuous-time martingale, (respectively, a family of measures parameterised by $t \in [0,T]$ which is increasing in convex order, or a double continuum of call prices) we construct a family…
In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…
How do multi-turn reasoning systems fail? The expected answer is logical contradiction, in which the system's maintained state becomes unsatisfiable. We show that the dominant mode is instead satisfiable drift, where the internal state…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
In the present paper we prove the compactness theorem with respect to partial structures and quasi-truth, using the technique of ultraproducts. Partial structures and quasi-truth are two notions developed within the partial structures…
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain…
In many applications, especially those involving prediction, models may yield near-optimal performance yet significantly disagree on individual-level outcomes. This phenomenon, known as predictive multiplicity, has been formally defined in…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
We consider a multivariate default system where random environmental information is available. We study the dynamics of the system in a general setting and adopt the point of view of change of probability measures. We also make a link with…
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility…
Let X and Y be an m-dimensional F-semimartingale and an n-dimensional H-semimartingale respectively on the same probability space, both enjoying the strong predictable representation property. We propose a martingale representation result…