Before revision:   Finally, we illustrate how investors with different  risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped distortion risk measures , and lower- and upper-tail  risk measures as examples.
After revision:  Finally, we illustrate how investors with different risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped distortion risk measures , and lower- and upper-tail distortion risk measures as examples.