Some inverse problem remarks of a continuous-in-time financial model in L^1([t_I,Theta_{max}])

: pp. 864–874
Received: February 13, 2023
Revised: June 13, 2023
Accepted: June 19, 2023
LGPM, CentraleSupélec, Université Paris-Saclay, Centre Européen de Biotechnologie et de Bioéconomie (CEBB), France

In the paper we are going to introduce an operator that is involved in the inverse problem of the continuous-in-time financial model.  This framework is designed to be used in the finance for any organization and, in particular, for local communities.  It allows to set out annual and multiyear budgets, with describing loan, reimbursement and interest payment schemes.  We discuss this inverse problem in the space of integrable functions over $\mathbb{R}$ having a compact support.  The concept of ill-posedness is examined in this space in order to obtain interesting and useful solutions.  Then, we will give some remarks for not functionality of the model for a given Repayment Pattern Density $\gamma$, when this operator is not invertible in the space.  Additionally, this inverse problem is illustrated in order to prove its ability to be used in a financial strategy.

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Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 864–874 (2023)