Related papers: What happens after a default: the conditional dens…

Stochastic processes with renewal properties are powerful tools for modeling systems where memory effects and long-time correlations play a significant role. In this work, we study a broad class of renewal processes where a variable's value…

The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state…

We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…

The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…

We discuss the equivalence of definitions for conditional Poisson processes, Cox processes, and stochastic intensities of point processes on the real line. We show that Watanabe's characterisation of conditional Poisson processes in terms…

This paper studies the consequences of capturing non-linear dependence among the covariates that drive the default of different obligors and the overall riskiness of their credit portfolio. Joint default modeling is, without loss of…

Interbank contagion can theoretically exacerbate losses in a financial system and lead to additional cascade defaults during downturn. In this paper we produce default analysis using both regression and neural network models to verify…

Extracting from shared resources requires making choices to balance personal profit and sustainability. We present the results of a behavioural experiment wherein we manipulate the default extraction from a finite resource. Participants…

Managing risk at the aggregate level is crucial for banks and financial institutions as required by the Basel III framework. In this paper, we introduce discrete time Bayesian state space models with Poisson measurements to model aggregate…

The research reveals the existence of a constant characteristic time of preparatory micro-structural processes before the onset of macro-failure at various high loading rates of brittle and quasi-brittle materials. The presence of this…

This paper is about Girsanov's theory. It (almost) doesn't contain new results but it is based on a simplified new approach which takes advantage of the (weak) extra requirement that some relative entropy is finite. Under this assumption,…

In this paper, we compare static and dynamic (reduced form) approaches for modeling wrong-way risk in the context of CVA. Although all these approaches potentially suffer from arbitrage problems, they are popular (respectively) in industry…

This paper provides an alternative approach to Duffie and Lando [Econometrica 69 (2001) 633-664] for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by constructing an economy…

Let $(X_t)_{t\ge0}$ be a continuous-time, time-homogeneous strong Markov process with possible jumps and let $\tau$ be its first hitting time of a Borel subset of the state space. Suppose $X$ is sampled at random times and suppose also that…

We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential…

Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…

We present a statistical test that can be used to verify supervisory requirements concerning overlapping time windows for the long-term calibration in rating systems. In a first step, we show that the long-run default rate is approximately…

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing…

This note aims to provide a basic intuition on the concept of filtrations as used in the context of reinforcement learning (RL). Filtrations are often used to formally define RL problems, yet their implications might not be eminent for…