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A new test of a wide class of interest rate models is proposed and applied to a recently developed quantum field theoretic model and the industry standard Heath-Jarrow-Morton model. This test is independent of the volatility function unlike…

We consider a microstructure foundation for rough volatility models driven by Poisson random measures. In our model the volatility is driven by self-exciting arrivals of market orders as well as self-exciting arrivals of limit orders and…

Existence of solutions to the Heath-Jarrow-Morton equation of the bond market with linear volatility and general L\'evy random factor is studied. Conditions for existence and non-existence of solutions in the class of bounded fields are…

We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…

We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact…

We present an overview of the broad class of financial models in which the prices of assets are L\'evy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is…

We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a time-dependent extended…

We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…

In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…

It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work…

We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson…

Based on ideas due to Scovel-Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov-Poisson system that exactly preserve that system's Hamiltonian structure. Notably, the technique applies in any space…

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random…

We analyze a coupled Cahn-Hilliard-Forchheimer system featuring concentration-dependent mobility, mass source and convective transport. The velocity field is governed by a generalized quasi-incompressible Forchheimer equation with…

We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary,…

We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps…

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily…

The Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions (PNP-FBV) describe ion transport with Faradaic reactions and have applications in a wide variety of fields. Using an adaptive time-stepper based…

This study develops an integrated stochastic modeling framework for pricing short and medium-maturity equity options and assessing interest-rate risk using the Heston (1993), Bates (1996), and CIR (1985) models. We calibrate the Heston…

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…