9 citations · 26 across the 36 of their papers we have counts for
44 papers
Global Structure and Local Specifications in Sublinear Valuation
Jongjin Park, David Criens, Hyungbin Park
This work studies the relationships among sublinear valuation rules, uncertainty structures, and local specifications in a time-homogeneous Markovian framework with killing. These…
An -Variational Formula on Wiener Space
David Criens, Carsten Hartmann, Michael Kupper
We establish a stochastic control representation for -norms on Wiener space. For every and every non-negative universally measurable functional , we show that $$\|φ…
On the hedging problem in general 1D diffusion markets
Alexis Anagnostakis, David Criens, Mikhail Urusov
We develop a PDE-based methodology for pricing and hedging European contingent claims in general one-dimensional diffusion markets characterized solely by their scale function and…
A Small-Noise Analysis of Controlled Functional Differential Equations with Gaussian Noise
David Criens, Max Nendel
We study small-noise asymptotics for controlled functional differential equations driven by additive Gaussian noise. The Gaussian noise is modeled on an abstract Wiener space, cove…
Risk-sensitive exit-time control for stochastic differential equations with path-dependent coefficients
David Criens, Fabian Fuchs
In this work, we study small-noise asymptotics of risk-sensitive exit-time control problems governed by stochastic differential equations with path-dependent coefficients. Our main…
On the structure of increasing profits in a 1D general diffusion market with interest rates
Alexis Anagnostakis, David Criens, Mikhail Urusov
In this paper, we investigate a financial market model consisting of a risky asset, modeled as a general diffusion parameterized by a scale function and a speed measure, and a bank…
On weak notions of no-arbitrage in a 1D general diffusion market with interest rates
Alexis Anagnostakis, David Criens, Mikhail Urusov
We establish deterministic necessary and sufficient conditions for the no-arbitrage notions "no increasing profit" (NIP), "no strong arbitrage" (NSA) and "no unbounded profit with…
Representation Theorems for Convex Expectations and Semigroups on Path Space
David Criens, Michael Kupper
The objective of this paper is to investigate the connection between penalty functions from stochastic optimal control, convex semigroups from analysis and convex expectations from…
No arbitrage and the existence of ACLMMs in general diffusion models
David Criens, Mikhail Urusov
In a seminal paper, F. Delbaen and W. Schachermayer proved that the classical NA ("no arbitrage") condition implies the existence of an "absolutely continuous local martingale meas…
On the representation property for 1D general diffusion semimartingales
David Criens, Mikhail Urusov
A general diffusion semimartingale is a one-dimensional path-continuous semimartingale that is also a regular strong Markov process. We say that a continuous semimartingale has the…
Stochastic optimal control problems with measurable coefficients and -drift
David Criens
We consider controlled stochastic differential equations (SDEs) with measurable coefficients, a uniformly elliptic diffusion coefficient and an -drift. No space-regularity wil…
Robust Market Convergence: From Discrete to Continuous Time
David Criens
Continuous time financial market models are often motivated as scaling limits of discrete time models. The objective of this paper is to establish such a connection for a robust fr…
A stochastic representation theorem for sublinear semigroups with non-local generators
David Criens, Lars Niemann
In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-Bellman operators. Our main result provides a stochastic represe…
Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs
David Criens, Moritz Ritter
We develop a limit theory for controlled path-dependent mean field stochastic partial differential equations (SPDEs) within the semigroup approach of Da Prato and Zabczyk. More pre…
Nonlinear Semimartingales and Markov Processes with Jumps
David Criens, Lars Niemann
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics. Here, the differential char…
A limit theory for controlled McKean-Vlasov SPDEs
David Criens
We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field…
Criteria for the absence of arbitrage in general diffusion markets
David Criens, Mikhail Urusov
We establish deterministic necessary and sufficient conditions for the no-arbitrage notions NA ("no arbitrage"), NUPBR ("no unbounded profit with bounded risk") and NFLVR ("no free…
A convergence theorem for Crandall-Lions viscosity solutions to path-dependent Hamilton-Jacobi-Bellman PDEs
David Criens
We establish a convergence theorem for Crandall-Lions viscosity solutions to path-dependent Hamilton-Jacobi-Bellman PDEs. Our proof is based on a novel convergence theorem for dyna…
Separating Times for One-Dimensional General Diffusions
David Criens, Mikhail Urusov
The separating time for two probability measures on a filtered space is an extended stopping time which captures the phase transition between equivalence and singularity. More spec…
Stochastic Processes under Parameter Uncertainty
David Criens
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a stochastic process with uncertain parameters. We develop a general framework whi…
Robust utility maximization with nonlinear continuous semimartingales
David Criens, Lars Niemann
In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncer…
A class of multidimensional nonlinear diffusions with the Feller property
David Criens, Lars Niemann
In this note we consider a family of nonlinear (conditional) expectations that can be understood as a multidimensional diffusion with uncertain drift and certain volatility. Here,…
Markov selections and Feller properties of nonlinear diffusions
David Criens, Lars Niemann
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a diffusion with uncertain local characteristics. Here, the differential character…
Nonlinear Continuous Semimartingales
David Criens, Lars Niemann
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differ…