On real growth and run-off companies in insurance ruin theory (Q2830886)

Solvency assessing of an insurance company is investigated by means of the ruin probability. In particular, if \(\{U_n: n=0,1,2,\dots\}\) is a real-valued stochastic process which depicts the development in time of the company's capital, the time of ruin is \(T=T_u\), where NEWLINE\[NEWLINET= \begin{cases} \inf \{n\in N; U_n<0\};\\ \infty \text{ if }U_n \geq0, \forall \in N.\end{cases}NEWLINE\]NEWLINE The focus of the paper is the ruin probability \(P(T<\infty)\) for large \(u\).NEWLINENEWLINEThe scenario considered throughout the paper takes into account several factors which impact on the business volume, determining its growth.NEWLINENEWLINEAsymptotic estimates for the ruin probability are obtained.NEWLINENEWLINEExamples in the last two sections complete the paper, illustrating the application of the basic results.