In the insurance business risky investments are dangerous

被引：0
|
作者：
Anna Frolova
Yuri Kabanov
Serguei Pergamenshchikov
机构：
[1] Alfa-Bank,
[2] Masha Poryvaeva str.,undefined
[3] 9,undefined
[4] 107078,undefined
[5] Moscow,undefined
[6] Russia ,undefined
[7] Laboratoire de Mathématiques,undefined
[8] Université de Franche-Comté,undefined
[9] 16 Route de Gray,undefined
[10] 25030 Besançon cedex,undefined
[11] France (e-mail: Youri.Kabanov@Math.Univ-FComte.FR) and Central Economics and Mathematics Institute,undefined
[12] Moscow,undefined
[13] Russia ,undefined
[14] Tomsk State University,undefined
[15] Lenin str.,undefined
[16] 36,undefined
[17] 634050 Tomsk,undefined
[18] Russia ,undefined
来源：
Finance and Stochastics | 2002年 / 6卷
关键词：
Key words: Risk process, geometric Brownian motion, ruin probabilities; JEL Classification: G22, G23; Mathematics Subject Classification (1991): 62P05,60J25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We find an exact asymptotics of the ruin probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Psi (u)$\end{document} when the capital of insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma>0$\end{document}. In contrast to the classical case of non-risky investments where the ruin probability decays exponentially as the initial endowment u tends to infinity, in this model we have, if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho:=2a/\sigma^2>1$\end{document}, that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Psi(u)\sim Ku^{1-\rho}$\end{document} for some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K>0$\end{document}. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho<1$\end{document}, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Psi(u)=1$\end{document}.
引用
收藏
页码：227 / 235
页数：8
相关论文
共 50 条
12345