439 citations · 1.3k across the 38 of their papers we have counts for
36 papers · 1 filter
Differentiability of quadratic forward-backward SDEs with rough drift
Peter Imkeller, Rhoss Likibi Pellat, Olivier Menoukeu Pamen
In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for {which} the drift in the forward equation does not satisfy the standard globally Lipschitz condition and t…
Hurst index estimation in stochastic differential equations driven by fractional Brownian motion
Jan Gairing, Peter Imkeller, Radomyra Shevchenko +1
We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malli…
Differentiability of SDEs with drifts of super-linear growth
Peter Imkeller, Gonçalo dos Reis, William Salkeld
We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin an…
Utility maximization via decoupling fields
Alexander Fromm, Peter Imkeller
We consider the utility maximization problem for a general class of utility functions defined on the real line. We rely on existing results which reduce the problem to a coupled fo…
Doubly Reflected BSDEs and -Dynkin games: beyond the right-continuous case
Miryana Grigorova, Peter Imkeller, Youssef Ouknine +1
We formulate a notion of doubly reflected BSDE in the case where the barriers and do not satisfy any regularity assumption and with a general filtration. Under a technical…
Optimal stopping with f -expectations: the irregular case
Miryana Grigorova, Peter Imkeller, Youssef Ouknine +1
We consider the optimal stopping problem with non-linear -expectation (induced by a BSDE) without making any regularity assumptions on the reward process . and with general f…
Reflected BSDEs when the obstacle is not right-continuous and optimal stopping
Miryana Grigorova, Peter Imkeller, Elias Offen +2
In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not…
A note on the Malliavin-Sobolev spaces
Peter Imkeller, Thibaut Mastrolia, Dylan Possamaï +1
In this paper, we provide a strong formulation of the stochastic G{â}teaux differentiability in order to study the sharpness of a new characterization, introduced in [6], of the Ma…
A Fourier approach to pathwise stochastic integration
Massimiliano Gubinelli, Peter Imkeller, Nicolas Perkowski
We develop a Fourier approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary…
An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift
Alexander Fromm, Peter Imkeller, David J. Prömel
We solve the Skorokhod embedding problem for a class of Gaussian processes including Brownian motion with non-linear drift. Our approach relies on solving an associated strongly co…
Existence of Lévy's area and pathwise integration
Peter Imkeller, David J. Prömel
Rough path analysis can be developed using the concept of controlled paths, and with respect to a topology in which Lévy's area plays a role. For vectors of irregular paths we inve…
Existence and stability of measure solutions for BSDE with generators of quadratic growth
Alexander Fromm, Peter Imkeller, Jianing Zhang
With an emphasis on generators with quadratic growth in the control variable we consider measure solutions of BSDE, a solution concept corresponding to the notion of risk neutral m…
Existence, Uniqueness and Regularity of Decoupling Fields to Multidimensional Fully Coupled FBSDEs
Alexander Fromm, Peter Imkeller
We develop an existence, uniqueness and regularity theory for general multidimensional strongly coupled FBSDE using so called decoupling fields. We begin with a local result and ex…
Paracontrolled distributions and singular PDEs
Massimiliano Gubinelli, Peter Imkeller, Nicolas Perkowski
We introduce an approach to study certain singular PDEs which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illus…
Solutions of martingale problems for Lévy-type operators and stochastic differential equations driven by Lévy processes with discontinuous coefficients
Peter Imkeller, Niklas Willrich
We show the existence of Lévy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with sta…
Large deviations for Hilbert space valued Wiener processes: a sequence space approach
Andreas Andresen, Peter Imkeller, Nicolas Perkowski
Ciesielski's isomorphism between the space of alpha-Hölder continuous functions and the space of bounded sequences is used to give an alternative proof of the large deviation princ…
2D- stochastic currents over the Wiener sheet
Franco Flandoli, Peter Imkeller, Ciprian Tudor
By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener-Itô integrals, we define a 2D-stochastic current over the Brownian sheet. This con…
Dimensional reduction in nonlinear filtering: A homogenization approach
Peter Imkeller, N. Sri Namachchivaya, Nicolas Perkowski +1
We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filte…
The Existence of Dominating Local Martingale Measures
Peter Imkeller, Nicolas Perkowski
We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is…
Forward-backward systems for expected utility maximization
Ulrich Horst, Ying Hu, Peter Imkeller +2
In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with gener…
On Malliavin's differentiability of BSDE with time delayed generators driven by Brownian motions and Poisson random measures
Łukasz Delong, Peter Imkeller
We investigate solutions of backward stochastic differential equations (BSDE) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute t…
Backward stochastic differential equations with time delayed generators - results and counterexamples
Łukasz Delong, Peter Imkeller
We deal with backward stochastic differential equations with time delayed generators. In this new type of equations, a generator at time t can depend on the values of a solution in…
Time irregularity of generalized Ornstein--Uhlenbeck processes
Z. Brzezniak, B. Goldys, P. Imkeller +3
The paper is concerned with the properties of solutions to linear evolution equation perturbed by cylindrical Lévy processes. It turns out that solutions, under rather weak require…
Differentiability of quadratic BSDEs generated by continuous martingales
Peter Imkeller, Anthony Réveillac, Anja Richter
In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of…