an:06730427
Zbl 1364.91071
Woo, Jae-Kyung; Xu, Ran; Yang, Hailiang
Gerber-Shiu analysis with two-sided acceptable levels
EN
J. Comput. Appl. Math. 321, 185-210 (2017).
00366758
2017
j
91B30 60K10 60K20
truncated Gerber-Shiu function; classical Poisson risk model; surplus-dependent premium rate; transition kernel; joint distribution of maximum and minimum before ruin; Markovian arrival process
Summary: In this paper, insurer's surplus process moved within upper and lower levels is analyzed. To this end, a truncated type of Gerber-Shiu function is proposed by further incorporating the minimum and the maximum surplus before ruin into the existing ones (e.g. [\textit{H. U. Gerber} and \textit{E. S. W. Shiu}, N. Am. Actuar. J. 2, No. 1, 48--78 (1998; Zbl 1081.60550); \textit{E. C. K. Cheung} et al., Insur. Math. Econ. 46, No. 1, 117--126 (2010; Zbl 1231.91157)]). A key component in our analysis of this proposed Gerber-Shiu function is the so-called transition kernel. Explicit expressions of the transition function under two different risk models are obtained. These two models are both generalizations of the classical Poisson risk model: (i) the first model provides flexibility in the net premium rate which is dependent on the surplus (such as linear or step function); and (ii) the second model assumes that claims arrive according to a Markovian arrival process (MAP). Finally, we discuss some applications of the truncated Gerber-Shiu function with numerical examples under various scenarios.
Zbl 1081.60550; Zbl 1231.91157