Causal operators (CO), such as various solution operators to stochastic differential
equations, play a central role in contemporary stochastic analysis; however, there is still no …

In this paper, we propose a new, information-based approach for modelling the dynamic
evolution of a portfolio of credit risky securities. In our setup, market prices of traded credit …

In this article we introduce and study a deep learning based approximation algorithm for
solutions of stochastic partial differential equations (SPDEs). In the proposed approximation …

We deal with the filtering problem of a general jump diffusion process, X, when the
observation process, Y, is a correlated jump diffusion process having common jump times …

Ziel dieses Kapitels ist die Anwendung der in den vorangegangenen Kapiteln hergeleiteten
Theorie auf die Bewertung von Kreditderivaten. Die Auswahl der Produkte und deren …

In this paper we study a nonlinear filtering problem for a general Markovian partially
observed system (X, Y), whose dynamics is modeled by correlated jump-diffusions having …

We investigate the risk control and dividend optimization problem of an insurance group in a
general setting and propose an innovative semi-analytical approach to the problem. The …

Deep Kalman filters (DKFs) are a class of neural network models that generate Gaussian
probability measures from sequential data. Though DKFs are inspired by the Kalman filter …

In problems involving control of financial processes, it is usually complicated to quantify
exactly the state variables. It could be expensive to acquire the exact value of a given state …

The two main approaches in credit risk are the structural approach pioneered by Merton and
the reduced‐form framework proposed by Jarrow and Turnbull and by Artzner and Delbaen …