Non-Cash Risk Measure on Nonconvex Sets

Chang Cong, Peibiao Zhao
2018 Mathematics  
Monetary risk measures are interpreted as the smallest amount of external cash that must be added to a financial position to make the position acceptable. In this paper, A new concept: non-cash risk measure is proposed and this measure provides an approach to transform the unacceptable positions into the acceptable positions in a nonconvex set. Non-cash risk measure uses not only cash but also other kinds of assets to adjust the position. This risk measure is nonconvex due to the use of
more » ... tion problem in L 1 norm. A convex extension of the nonconvex risk measure is derived and the relationship between the convex extension and the non-cash risk measure is detailed.
doi:10.3390/math6100186 fatcat:dwkgg36yxnglvh3raoppddqvd4