MOCT | Spectral Theory of Non-Selfadjoint Markov Processes with Applications in Self-Similarity, Branching Processes and Financial Mathematics

Summary
The project contextually sets up a novel framework to study the spectral-theoretical properties of classes of non-selfadjoint (NSA) operators related to Markov processes (MP) via their intertwining to a continuous path selfadjoint (SA) MP. Conceptually, this means that the jumps of each class of NSA MP can be considered a perturbation of one SA MP realized by an intertwining kernel. This approach can have far-reaching consequences for understanding classes of MP as the reduction to SA MP leads to well-studied objects whereas the spectral theory of NSA operators is far from understood. The price of that is the non-invertability of the intertwining kernels. This framework is explored and crystallized by a challenging,
detailed spectral-theoretical study of an enormous class of NSA operators directly arising from the key phenomenon of self-similarity and in duality from branching. This is achieved by a synergy of research fields complementing each other to obtain the spectral properties of those operators culminating in the derivation of spectral expansions of the generated semigroups. As a result of this synergy, a number of tools and techniques with impact, including applications to fields beyond the scope of the project, are derived. A particular development in the area of recurrent equations and special functions will be unexpectedly exploited to the effect of a comprehensive theoretical and applied study, including numerical schemes, of
key quantities in financial and insurance mathematics such as Asian options and perpetuities. A training-through-research in line with the fellow’s affiliation to the host institution and the proposed secondment will critically contribute to the optimal completion of the proposal in terms of time, scope and quality.
Unfold all
/
Fold all
More information & hyperlinks
Web resources: https://cordis.europa.eu/project/id/657025
Start date: 01-07-2015
End date: 30-06-2017
Total budget - Public funding: 128 994,00 Euro - 128 994,00 Euro
Cordis data

Original description

The project contextually sets up a novel framework to study the spectral-theoretical properties of classes of non-selfadjoint (NSA) operators related to Markov processes (MP) via their intertwining to a continuous path selfadjoint (SA) MP. Conceptually, this means that the jumps of each class of NSA MP can be considered a perturbation of one SA MP realized by an intertwining kernel. This approach can have far-reaching consequences for understanding classes of MP as the reduction to SA MP leads to well-studied objects whereas the spectral theory of NSA operators is far from understood. The price of that is the non-invertability of the intertwining kernels. This framework is explored and crystallized by a challenging,
detailed spectral-theoretical study of an enormous class of NSA operators directly arising from the key phenomenon of self-similarity and in duality from branching. This is achieved by a synergy of research fields complementing each other to obtain the spectral properties of those operators culminating in the derivation of spectral expansions of the generated semigroups. As a result of this synergy, a number of tools and techniques with impact, including applications to fields beyond the scope of the project, are derived. A particular development in the area of recurrent equations and special functions will be unexpectedly exploited to the effect of a comprehensive theoretical and applied study, including numerical schemes, of
key quantities in financial and insurance mathematics such as Asian options and perpetuities. A training-through-research in line with the fellow’s affiliation to the host institution and the proposed secondment will critically contribute to the optimal completion of the proposal in terms of time, scope and quality.

Status

CLOSED

Call topic

MSCA-IF-2014-EF

Update Date

28-04-2024
Images
No images available.
Geographical location(s)
Structured mapping
Unfold all
/
Fold all
Horizon 2020
H2020-EU.1. EXCELLENT SCIENCE
H2020-EU.1.3. EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (MSCA)
H2020-EU.1.3.2. Nurturing excellence by means of cross-border and cross-sector mobility
H2020-MSCA-IF-2014
MSCA-IF-2014-EF Marie Skłodowska-Curie Individual Fellowships (IF-EF)