I see two things you can try.
1) Activate RGBA mode for better resolution detectionC:\Program Files (x86)\Steam\SteamApps\common\f.e.a.r. 3\options.cfg
Uncomment -forcergbamode and give it a try.
2) Hex-edit the config file%APPDATA%\Day 1 Studios\FEAR3\SharedData.settings
This is where the resolution setting is stored (in hexadecimal form).
4800 (dec) is 12c0 (hex), so
search the file for c0 12 (BigEndian).
5100 (dec) is 13ec (hex), so
replace c0 12 with ec 13 (BigEndian).
If you have problems with this feel free to PM me your config file.
Either way please let me know how it goes, there's
another thread about this but no confirmed solution yet.