Related papers: A Note on Real-World and Risk-Neutral Dynamics for…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX,…
An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is…
An extension of the Heath--Jarrow--Morton model for the development of instantaneous forward interest rates with deterministic coefficients and Gaussian as well as L\'evy field noise terms is given. In the special case where the L\'evy…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
Discount is the difference between the face value of a bond and its present value. I propose an arbitrage-free dynamic framework for discount models, which provides an alternative to the Heath--Jarrow--Morton framework for forward rates. I…
The problem of existence of arbitrage free and monotone CDO term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates with the use of the…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a…
We study the loss, recovery, and preservation of differentiability of time-dependent large deviation rate functions. This study is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient of the rate-function evolves according to a…
Especially in the insurance industry interest rate models play a crucial role e.g. to calculate the insurance company's liabilities, performance scenarios or risk measures. A prominant candidate is the 2-Additive-Factor Gaussian Model…
We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift,…
In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread,…
We propose a new class of financial volatility models, called the REcurrent Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis and out-ofsample forecasting of the traditional conditional heteroskedastic models. In…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
This work provides a framework for data-driven control of discrete time systems with unknown input-output dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control of the system such that a…
In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First,…
We consider the Regge-Teitelboim model for a relativistic extended object embedded in a fixed background Minkowski spacetime, in which the dynamics is determined by an action proportional to the integral of the scalar curvature of the…