SET-VALUED DYNAMIC RISK MEASURES FOR BOUNDED DISCRETE-TIME PROCESSES

Yanhong Chen and Yijun Hu ()
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Yanhong Chen: College of Finance and Statistics, Hunan University, Changsha 410082, P. R. China
Yijun Hu: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 03, 1-42

Abstract: In this paper, we study how to evaluate the risk of a financial portfolio, whose components may be dependent and come from different markets or involve more than one kind of currencies, while we also take into consideration the uncertainty about the time value of money. Namely, we introduce a new class of risk measures, named set-valued dynamic risk measures for bounded discrete-time processes that are adapted to a given filtration. The time horizon can be finite or infinite. We investigate the representation results for them by making full use of Legendre–Fenchel conjugation theory for set-valued functions. Finally, some examples such as the set-valued dynamic average value at risk and the entropic risk measure for bounded discrete-time processes are also given.

Keywords: Dynamic risk measures; set-valued risk measures; bounded discrete-time processes; representation results (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S021902492050017X

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