I've been looking into this a bit due to my brother being asthmatic (and a carefree asshat). There isn't anything definitive, but it seems to very much depend on how serious your asthma is along with how old you are. If you have poorly controlled asthma or have to take steroid pills then the NHS defines you along with COPD sufferers as being in a high risk group. Those that are inhaler only are not given any specific guidance other than to be wary.
Actual research is thin on the ground and I haven't managed to come across a study that specifically isolates asthmatics as a group, let alone stratifies them by severity. The nearest I've got is this study that I posted on March 11th:
Comorbidity and its impact on 1,590 patients with COVID-19 in China: A Nationwide Analysis
Here's the relevant table from that study (need to remember that it is a very rough guide):
As you can see Asthma isn't covered, only people with COPD. What this basically says is that people with COPD are roughly 2.681 times more likely to die than a healthy person in the same age group. Note the confidence interval is very wide indeed here, and the study can only say with 95% certainty that the true hazard ratio lies somewhere between 1.424 and 5.048.
This doesn't correspond 1:1 to the hazard ratio associated with severe asthma and represents the very worst estimate an asthma sufferer would have. It will vastly overstate the risk associated with milder asthma. In terms of studies around this area though it's the best I've got as of now.
It's also important to note that there is no evidence of people with asthma being more prone to contracting the disease, and that Asthma UK and ACAII (the Yank one) both say that there is no elevated risk from continuing to take your medication.
@mehdimike