Higher strong order methods for linear Itô SDEs on matrix Lie groups

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate

doi:10.1007/s10543-021-00905-9

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…As this approach preserves the geometry of the Lie group G opposed to applying the Euler-Maruyama scheme directly to (3.2), this method was called the geometric Euler-Maruyama scheme in [13]. Higher order schemes based on this approach can be found in [14].…”

Section: Sdes On the Lie Group Of Stochastic Matricesmentioning

confidence: 99%

A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups

Kamm¹,

Muniz²

2022

Preprint

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In this paper, we introduce a novel methodology to model rating transitions with a stochastic process. To introduce stochastic processes, whose values are valid rating matrices, we noticed the geometric properties of stochastic matrices and its link to matrix Lie groups. We give a gentle introduction to this topic and demonstrate how Itô-SDEs in R will generate the desired model for rating transitions.To calibrate the rating model to historical data, we use a Deep-Neural-Network (DNN) called TimeGAN to learn the features of a time series of historical rating matrices. Then, we use this DNN to generate synthetic rating transition matrices. Afterwards, we fit the moments of the generated rating matrices and the rating process at specific time points, which results in a good fit.After calibration, we discuss the quality of the calibrated rating transition process by examining some properties that a time series of rating matrices should satisfy, and we will see that this geometric approach works very well.

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Section: Sdes On the Lie Group Of Stochastic Matricesmentioning

confidence: 99%

A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups

Kamm¹,

Muniz²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [13] the authors show a stochastic extension of this result, that is, a matrix exponential representation of type (1.1) for the solutions of (1.2) for non-commuting matrices A and B formulated for equations in the Itô sense. See also [15,17,21,22].…”

Section: Introductionmentioning

confidence: 99%