SCROLLER  A Stochastic ContROL approach to machine Learning with applications to Environmental Risk models
About the project
The main idea of the SCROLLER project is to study the connections between stochastic analysis, risk theory and machine learning.
Stochastic analysis is the mathematical study of uncertainty over time. In particular, stochastic optimal control theory is a tool for making optimal decisions over time under uncertainty. The reason for working with stochastic models, as opposed to deterministic ones, is that most reallife problems are influenced by uncertain factors. Weather, politics, climate change and human actions are potential sources of uncertainty.
During the last decade, there has been a vast technological development and growth in computational power. In addition, digitization implies that
big data is available in many different settings. Machine learning is a set of mathematical algorithms and techniques which enable computers to improve at performing tasks with experience. Examples of ML algorithms are neural networks and reinforcement learning.
Machine learning algorithms can lead to wrong conclusions if we are
not careful in understanding the underlying mathematics. Though the experimental results of machine learning are good, there is still a lack of understanding of the mathematical reasons for these results. In particular, the literature concerning the connections between machine learning and stochastic analysis is sparse. The main purpose of the SCROLLER project is to study these connections.
In choice of applications throughout the SCROLLER project, we will focus on problems related to environmental and climate risks. For instance, we
will work on degradation models with respect to environmental risk factors. We will use environmental contours for safer risk assessment of structures exposed to extreme environmental events. Due to climate change, there is more extreme weather, and in general more uncertainty regarding the future. We hope that this project can contribute to derive suitable risk assessments which take this change into account.
Financing
This project is funded by the Reseach Council of Norway . Funding ID: 299897
Publications
 Agrell, Christian & Dahl, Kristina Rognlien (2021). Sequential Bayesian optimal experimental design for structural reliability analysis. Statistics and computing . ISSN 09603174. 31 . doi: 10.1007 / s11222021100002 Full text in knowledge archive .
 Dahl, Kristina Rognlien & Eyjolfsson, Heidar (2021). Selfexciting jump processes as deterioration models, to be published in Proceedings of the 31st European Safety and Reliability Conference. Edited by B. Castanier, M. Cepin, D. Bigaud & C. Berenguer, Research Publishing, Singapore, ISBN: 9819730000000. doi: 10.3850 / 9819730000000.
 Savku E. (2021). Fundamentals of Market Making via Stochastic Optimal Control, (Book Chapter) Submitted.

Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2022). Stochastic Modeling of Stratospheric Temperature. Mathematical Geosciences. ISSN 18748961. 54, p. 651–678. doi: 10.1007/s11004021099906. Full text in Research Archive Show summary

Agrell, Christian & Dahl, Kristina Rognlien (2021). Sequential Bayesian optimal experimental design for structural reliability analysis. Statistics and computing. ISSN 09603174. 31. doi: 10.1007/s11222021100002. Full text in Research Archive

Dahl, Kristina Rognlien (2020). Forwardbackward stochastic differential equation games with delay and noisy memory. Stochastic Analysis and Applications. ISSN 07362994. 38(4), p. 708–729. doi: 10.1080/07362994.2020.1713810. Full text in Research Archive

Dahl, Kristina Rognlien & Huseby, Arne (2020). Environmental contours and optimal design. In Baraldi, Piero; Di Maio, Francesco P. & Zio, Enrico (Ed.), eproceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference (ESREL2020 PSAM15). Research Publishing Services. ISSN 9789811485930. p. 3233–3240.

Savku, Emel (2022). A Constrained NonzeroSum Stochastic Differential Game Application.

Savku, Emel (2022). An Application of Stochastic Differential Games with Lagrange Multipliers:Bancassurance.

Savku, Emel (2022). A constrained stochastic differential game application: Bancassurance.

Savku, Emel (2022). An Application of Stochastic Differential Games with Lagrange Multipliers: Bancassurance.

Savku, Emel (2021). Stochastic Maximum Principle with Regimes and Memory.

Savku, Emel (2021). Stochastic Differential Games via Dynamic Programming Principle with Regimes.

Savku, Emel (2021). A Nonzerosum Game Formulation for a Markov RegimeSwitching Portfolio Strategy.

Savku, Emel (2021). Portfolio Strategies via Stochastic Differential Games with Regimes.

Dahl, Kristina Rognlien & Eyolfsson, Heidar (2021). Selfexciting jump processes as deterioration models.

Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2021). Stochastic modelling of stratospheric temperature.

Savku, Emel (2021). Stochastic Optimal Control Techniques for a RegimeSwitching Model with Applications in Finance.

Savku, Emel (2021). An Application of Stochastic Maximum Principle with Regimes and Memory.

Savku, Emel (2021). Stochastic Differential Games within the framework of RegimeSwitches.

Dahl, Kristina Rognlien (2020). The SCROLLER project A Stochastic ContROL approach to machine Learning with applications to Environmental Risk models.

Dahl, Kristina Rognlien (2020). FBSDE games with delay & noisy memory.

Dahl, Kristina Rognlien (2020). The SCROLLER project and a subproject: Optimal design.

Dahl, Kristina Rognlien & Huseby, Arne (2020). Environmental contours and optimal design.