@article {10.3844/jmssp.2022.143.147,
article_type = {journal},
title = {Mathematical Approach to the Ruin Problem with Compounding Assets},
author = {Orukari, Mercy Amaebi},
volume = {18},
year = {2022},
month = {Oct},
pages = {143-147},
doi = {10.3844/jmssp.2022.143.147},
url = {https://thescipub.com/abstract/jmssp.2022.143.147},
abstract = {This study considered the Ruin problem with an income process with stationary independent increments. The characterization is obtained which is general for the probability of $r(y)$, that the asset of a firm will never be zero whenever the initial asset level of the firm is $y$. The aim of this study is also to determine $r(y) = P \{ T < \infty | Y(0) = y \}$, If we let $T = inf \{ t \ge 0; Y(t) < 0 \}$, A condition that is necessary and sufficient is studied for a distribution that is one – dimensional of $X_N$ which coverages to $X_*$. The result that is obtained concerning the probability, is of ruin before time $t$. Riemann-Stieltjes integral, two functions $f$ and with symbol as $\int_a^b f(x)da(x)$ was used and is a special case in which $a() = x$, where $a$ has a continuous derivative. It is defined such that the Stieltjes integral $\int_a^b f(x)da(x)$ becomes the Riemann integral $\int_a^b f(x)a^| d(x)$.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}