A Neural RDE approach for continuous-time non-Markovian stochastic control problems
M Hoglund, E Ferrucci, C Hernández… - arXiv preprint arXiv …, 2023 - arxiv.org
We propose a novel framework for solving continuous-time non-Markovian stochastic control
problems by means of neural rough differential equations (Neural RDEs) introduced in …
problems by means of neural rough differential equations (Neural RDEs) introduced in …
Portfolio optimization in fractional and rough Heston models
N Bäuerle, S Desmettre - SIAM Journal on Financial Mathematics, 2020 - SIAM
We consider a fractional version of the Heston volatility model which is inspired by [H.
Guennoun et al., SIAM J. Financial Math,, 9 (2018), pp. 1017--1045]. Within this model we …
Guennoun et al., SIAM J. Financial Math,, 9 (2018), pp. 1017--1045]. Within this model we …
Reflected backward stochastic differential equations with rough drivers
H Li, H Zhang, K Zhang - arXiv preprint arXiv:2407.17898, 2024 - arxiv.org
In this paper, we study reflected backward stochastic differential equations driven by rough
paths (rough RBSDEs), which can be understood as a probabilistic representation of …
paths (rough RBSDEs), which can be understood as a probabilistic representation of …
Stochastic Control with Signatures
P Bank, C Bayer, PP Hager, S Riedel… - arXiv preprint arXiv …, 2024 - arxiv.org
This paper proposes to parameterize open loop controls in stochastic optimal control
problems via suitable classes of functionals depending on the driver's path signature, a …
problems via suitable classes of functionals depending on the driver's path signature, a …
Utility maximization in multivariate Volterra models
F Aichinger, S Desmettre - SIAM Journal on Financial Mathematics, 2023 - SIAM
This paper is concerned with portfolio selection for an investor with power utility in multiasset
financial markets in a rough stochastic environment. We investigate Merton's portfolio …
financial markets in a rough stochastic environment. We investigate Merton's portfolio …
Pathwise stochastic control with applications to robust filtering
We study the problem of pathwise stochastic optimal control, where the optimization is
performed for each fixed realisation of the driving noise, by phrasing the problem in terms of …
performed for each fixed realisation of the driving noise, by phrasing the problem in terms of …
Robustness of Optimal Controlled Diffusions with Near-Brownian Noise via Rough Paths Theory
In this article we show a robustness theorem for controlled stochastic differential equations
driven by approximations of Brownian motion. Often, Brownian motion is used as an …
driven by approximations of Brownian motion. Often, Brownian motion is used as an …
Controlled viscosity solutions of fully nonlinear rough PDEs
M Gubinelli, S Tindel, I Torrecilla - arXiv preprint arXiv:1403.2832, 2014 - arxiv.org
We propose a definition of viscosity solutions to fully nonlinear PDEs driven by a rough path
via appropriate notions of test functions and rough jets. These objects will be defined as …
via appropriate notions of test functions and rough jets. These objects will be defined as …
Pathwise stochastic control and a class of stochastic partial differential equations
N Bhauryal, AB Cruzeiro, C Oliveira - Journal of Optimization Theory and …, 2024 - Springer
In this article, we study a stochastic optimal control problem in the pathwise sense, as
initially proposed by Lions and Souganidis in [CR Acad. Sci. Paris Ser. I Math., 327 (1998) …
initially proposed by Lions and Souganidis in [CR Acad. Sci. Paris Ser. I Math., 327 (1998) …