The bandwidth is in the range of 100s of MHz. The photodiode is reverse biased. A voltage amplifier is another possible approach, however, I would like for the amplified signal to have a linear response with respect to the input current.
What is the bandwidth of your application?
At DC through audio frequencies the impedance of common small coaxial connectors is merely a shunt capacitance. Similarly, short coaxial cables are capacitive at low frequencies.
Is your photodiode reverse-biased (with relatively low capacitance) or in zero-bias (photovoltaic) mode with higher capacitance and lower shunt resistance?
At higher bandwidth, it is normal to run the photodiode with reverse bias into a 50 ohm termination rather than into a TIA.
If you run a reverse-biased photodiode into a 50 ohm load, the response will be linear so long as the voltage developed across the load is small compared with the reverse bias.
The simplified model of the photodiode is a current generator with a parasitic diode (to the bias supply); the parasitic diode can be modeled roughly as a high resistance in parallel with a voltage-dependent capacitance, so long as the net reverse voltage is reasonably high.
The net capacitance of the diode (small) with the 50 ohms (assuming a matched transmission line and coax connectors) will limit the high frequency response.
This approach does not have the stability problem of the TIA with shunt capacitance, but that can be avoided with careful detailed design.