Mathematical Approach to the Ruin Problem with Compounding Assets

Thisstudy considered the Ruin problem with an income process stationaryindependent increments. The characterization is obtained which general forthe probability of r(y), that asset a firm will never bezero whenever initial level y. aim this studyis also to determine r(y) = P{T < ¥ | Y(0)= y}, If we let T inf{t ≥ 0; Y(t)< 0}, A condition necessary and sufficient studied for adistribution one – dimensional Xn coveragesto X*.The result concerning probability,is ruin before time t. Riemann-Stieltjes integral, two functions fand symbol as was used special case in a() =x, where hasa continuous derivative. It defined such Stieltjes integral becomes Riemann integral.