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A MARTINGALE APPROACH TO A RUIN MODEL WITH SURPLUS FOLLOWING A COMPOUND POISSON PROCESS  

Oh, Soo-Mi (Department of Statistics, Sookmyung Women's University)
Jeong, Mi-Ock (Department of Statistics, Sookmyung Women's University)
Lee, Eui-Yong (Department of Statistics, Sookmyung Women's University)
Publication Information
Journal of the Korean Statistical Society / v.36, no.2, 2007 , pp. 229-235 More about this Journal
Abstract
We consider a ruin model whose surplus process is formed by a compound Poisson process. If the level of surplus reaches V > 0, it is assumed that a certain amount of surplus is invested. In this paper, we apply the optional sampling theorem to the surplus process and obtain the expectation of period T, time from origin to the point where the level of surplus reaches either 0 or V. We also derive the total and average amount of surplus during T by establishing a backward differential equation.
Keywords
Backward differential equation; compound Poisson process; optional sampling theorem; surplus process.;
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