Atstatymo lygties sprendinio aproksimavimas klasikiniame rizikos modelyje /

The main objective of this work is to derive numerical methods from the renewal equation of Cramér – Lundberg model that would approximate the probability of ultimate ruin for any loss distribution, along with empirical method analysis. By employing the recovery equation, three expressions for ψ(u) are derived analytically for testing when claims are distributed according to: exponential distribution, mixture of two exponential distributions, and the second Erlang distribution. Subsequently, utilizing classical numerical integration schemes such as left and right Riemann sums, trapezoidal rule, and Simpson’s rule, four methods suitable for the recovery equation are derived. We empirically assess the convergence rate of the methods, determine the step sizes h for which the methods are stable, and propose possible implementations to reduce time complexity: online fast Fourier transform and solved recursion. Additionally, we provide the R program code, naive implementation of all four methods, and one of solved recursion.

Grantor dc:publisher

Institutional Repository of Vilnius University

Year dc:date

2024

Author dc:creator

• Lukoševičius, Gustas,

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

lit

Repository record dc:identifier

https://repository.vu.lt/VU:ELABAETD210642105&prefLang=en_US

OAI identifier oai:identifier

oai:vu.lt:elaba:210642105