Solving the Sturm-Liouville problem by three-point difference schemes of high order of accuracy

For the solving Sturm-Liouville problem, three-point difference schemes of high order of accuracy on a nonuniform grid are constructed. It is shown that the coefficients of these schemes are expressed in terms of solutions of two auxiliary initial value problems. An estimate of the accuracy of three-point difference schemes is obtained and an iterative Newton method is proposed to determine their solution. Numerical experiments confirm theoretical conclusions.

The Concept of a Multi-Level Optimization Model of the Centrifugal Compressor Workflow

The paper presents the main ideas of the virtual test bench concept for rapid obtaining of the reliable characteristics of compressors based on a multi-level mathematical model with a two-step identification using data obtained from mathematical models with a high order of accuracy. One of the possible identification algorithms and the results of its successful testing are given on the example of a centrifugal compressor stage developed and tested at NASA.

An Accurate Solution for Credit Valuation Adjustment (CVA) and Wrong Way Risk

This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of accuracy with a relatively easy implementation. We find that the valuation of a defaultable derivative is normally determined via backward induction when their payoffs could be positive or negative. Moreover, the model can naturally capture wrong or right way risk. https://osf.io/preprints/socarxiv/3yjk2/download

An Accurate Solution for Credit Valuation Adjustment (CVA) and Wrong Way Risk

This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of accuracy with a relatively easy implementation. We find that the valuation of a defaultable derivative is normally determined via backward induction when their payoffs could be positive or negative. Moreover, the model can naturally capture wrong or right way risk.