Computation of distorted probabilities for diffusion processes via stochastic control methods

We study distorted survival probabilities related to risks in incomplete markets. The risks are modeled as diffusion processes, and the distortions are of general type. We establish a connection between distorted survival probabilities of the original risk process and distortion-free survival probabilities of new pseudo risk diffusions; the latter turns out to be diffusions with killing or splitting rates related, respectively, to concave and convex distortions. The main tools come from the theories of stochastic control, stochastic differential games, and non-linear partial differential equations.