I am working as a professor in mathematics at BI Norwegian Business School. I hold a Ph.D in Mathematics from the University of Oslo, where I specialized in stochastic analysis and financial mathematics.
My research is mostly focused around various topics in the field of stochastic analysis and rough path theory, and the application of these theories towards financial modelling and data science.
In the acameic year of 2023/2024 I am leading the Signatures for Images project at the Centre of Advanced Studies(CAS) together with Prof. Kurusch Ebrahimi-Fard (NTNU). See here for more information. I will therefore be located at The Norwegian Academy of Sciences and Letters during this year.
I am very interested in discussing applications of mathematical theory towards real cases arising in the financial industry, be it related to risk and portfolio management or trading. Please do not hestiate to get in touch if you are wondering about anything related to financial mathamtics or risk management.
We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stoch Process Appl 126(8):2323–2366, 2016). To this end, we extend the notion of non-linear Young equations to a two dimensional domain and prove existence and uniqueness of such equations. This concept is then used in order to prove regularization by noise for stochastic equations on the plane. The statement of regularization by noise is formulated in terms of the regularity of the local time associated to the perturbing stochastic field. For this, we provide two quantified example: a fractional Brownian sheet and the sum of two one-parameter fractional Brownian motions. As a further illustration of our regularization results, we also prove well-posedness of a 1D non-linear wave equation with a noisy boundary given by fractional Brownian motions. A discussion of open problems and further investigations is provided.
Harang, Fabian Andsem & Mayorcas, Avi (2023)
Pathwise regularisation of singular interacting particle systems and their mean field limits
This article is devoted to the extension of the theory of rough paths in the context of Volterra equations with possibly singular kernels. We begin to describe a class of two parameter functions defined on the simplex called Volterra paths. These paths are used to construct a so-called Volterra-signature, analogously to the signature used in Lyon’s theory of rough paths. We provide a detailed algebraic and analytic description of this object. Interestingly, the Volterra signature does not have a multiplicative property similar to the classical signature, and we introduce an integral product behaving like a convolution extending the classical tensor product. We show that this convolution product is well defined for a large class of Volterra paths, and we provide an analogue of the extension theorem from the theory of rough paths (which guarantees in particular the existence of a Volterra signature). Moreover the concept of convolution product is essential in the construction of Volterra controlled paths, which is the natural class of processes to be integrated with respect to the driving noise in our situation. This leads to a rough integral given as a functional of the Volterra signature and the Volterra controlled paths, combined through the convolution product. The rough integral is then used in the construction of unique solutions to Volterra equations driven by Hölder noises with singular kernels. An example concerning Brownian noises and a singular kernel is treated.
Harang, Fabian Andsem & Benth, Fred Espen (2021)
Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise - Probabilistic Properties and Applications