I am studying the differences in bayesian and frequentist approaches to point estimation.
I understand that there are objective and subjective approaches to Bayesian and some people don't like the subjective point of view.
Putting the subjectivity of choosing a prior aside (which I am not that uncomfortable with), I am mostly puzzled with the subjectivity of Bayesian risk.
Bayesian posterior risk is defined as follow
$R(\theta,\delta) = \int L(\theta,\delta(x))p(\theta|x)d\theta$
where posterior is computed with the Bayes formula.
Since the posterior is calculated starting from our subjective prior, our risk becomes subjective as well. Different priors yield different risks. This sounds strange because the real risk should be with respect to the loss function $L$, and choice of $\delta$; and it should be based on the true state of nature, not on our bliefs. Moreover this is not formulated as a relative risk of our belief with respect to the real risk. It is formulated as if we are dictating our belief as the real risk. This sounds to me more theological than scientific.
How do Bayesians reconcile this issue, or what is the rationale?