Coherent and convex monetary risk measures for unbounded càdlàg processes View Full Text


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Article Info

DATE

2005-07

AUTHORS

Patrick Cheridito, Freddy Delbaen, Michael Kupper

ABSTRACT

.Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all càdlàg processes that are adapted to a given filtration. We show that if such risk measures are required to be real-valued, then they can only depend on a stochastic process in a way that is uninteresting for many applications. Therefore, we allow them to take values in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(- \infty, \infty]$\end{document}. The economic interpretation of a value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\infty$\end{document} is that the corresponding financial position is so risky that no additional amount of money can make it acceptable. The main result of the paper gives different characterizations of coherent or convex monetary risk measures on the space of all bounded adapted càdlàg processes that can be extended to coherent or convex monetary risk measures on the space of all adapted càdlàg processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded càdlàg processes induced by a so called m-stable set. More... »

PAGES

369-387

References to SciGraph publications

  • 2000-10. Coherent risk measures in BLÄTTER DER DGVFM
  • 2002. Coherent Risk Measures on General Probability Spaces in ADVANCES IN FINANCE AND STOCHASTICS
  • 2006. The Structure of m–Stable Sets and in Particular of the Set of Risk Neutral Measures in IN MEMORIAM PAUL-ANDRÉ MEYER
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    http://scigraph.springernature.com/pub.10.1007/s00780-004-0150-7

    DOI

    http://dx.doi.org/10.1007/s00780-004-0150-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1048590037


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