INVERSE PROBLEM STABILITY OF A CONTINUOUS-IN-TIME FINANCIAL MODEL

Inverse problem stability of a continuous-in-time financial model

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 spaceM([tI,Θmax]), and in Hilbert space L([tI,Θmax]) when they are density measures. For this inverse problem we prove the uniqueness the...

Inverse problem and concentration method of a continuous-in-time financial model

In a continuous-in-time model there is the important financial quantity called Loan which can not be determined directly in terms of Algebraic Spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a n...

The stability of the solution of an inverse spectral problem with a singularity

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

Stability of the Parareal Time Discretization for Parabolic Inverse Problem

The practical aspect in the parareal algorithm that it consist of using two solvers over different time stepping, the coarse and fine solvers to produce a rapid convergent iterative method for multi processors computations. The coarse solver solve the equation sequentially on the coarse time step while the fine solver use the information from the coarse solution to solve, in parallel, over the ...

Financial Mathematics in Continuous Time