There are a fair number of outstanding security issues in the Linux kernel for Debian 8 "jessie", but none of them were considered serious enough to issue a security update and DSA. Instead, most of them are being fixed through the point release (8.7) which will be released this weekend. Don't forget that you need to reboot to complete a kernel upgrade.

This update to linux (version 3.16.39-1) also adds the perf security mitigation feature from Grsecurity. You can disable unprivileged use of perf entirely by setting sysctl kernel.perf_event_paranoid=3. (This is the default for Debian "stretch".)