# Inverse Problem Stability of a Continuous-in-Time Financial Model

Authors
• 1 Chemin de Beaulieu, Piaf INRA, Site de Crouël 5, Clermont-Ferrand, 63000, France , Clermont-Ferrand (France)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jul 10, 2019
Volume
39
Issue
5
Pages
1423–1439
Identifiers
DOI: 10.1007/s10473-019-0519-5
Source
Springer Nature
Keywords
In this work, we study the inverse problem stability of the continuous-in-time model which is designed to be used for the finances of public institutions. We discuss this study with determining the Loan measure from algebraic spending measure in Radon measure space M([tI,Θmax])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{M}([t_I,\;\Theta_{\text{max}}])$$\end{document}, and in Hilbert space L2([tI,Θmax])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{L}^{2}([t_I,\;\Theta_{\text{max}}])$$\end{document} when they are density measures. For this inverse problem we prove the uniqueness theorem, obtain a procedure for constructing the solution and provide necessary and sufficient conditions for the solvability of the inverse problem in L2([tI,Θmax])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{L}^{2}([t_I,\;\Theta_{\text{max}}])$$\end{document}.