 Entrance times of random walks: With applications to pension fund modelingSøren Fiig Jarner and Morten Tolver Kronborg Insurance: Mathematics and Economics, 2016, vol. 67, issue C, 1-20 Abstract: The purpose of the paper is twofold. First, we consider entrance times of random walks, i.e. the time of first entry to the negative axis. Partition sum formulas are given for entrance time probabilities, the nthderivative of the generating function, and the nthfalling factorial entrance time moment. Similar formulas for the characteristic function of the position of the random walk both conditioned on entry and conditioned on no entry are also established. Second, we consider a model for a with-profits collective pension fund. The model has previously been studied by approximate methods, but we give here an essentially complete theoretical description of the model based on the entrance time results. We also conduct a mean–variance analysis for a fund in stationarity. To facilitate the analysis we devise a simple and effective exact simulation algorithm for sampling from the stationary distribution of a regenerative Markov chain. Keywords: Random walks; Entrance times; Factorial moment; Partition sum; Stationarity; Exact simulation; Collective pension fund; With-profits contracts (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:67:y:2016:i:c:p:1-20 DOI: 10.1016/j.insmatheco.2015.11.006 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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