Computation of distorted probabilities for diffusion processes via stochastic control methods

We study distorted survival probabilities related to risks in incomplete ma rkets. The risks are modeled as diffusion processes, and the distortions ar e of general type. We establish a connection between distorted survival pro babilities of the original risk process and distortion-free survival probab ilities of new pseudo risk diffusions; the latter turns out to be diffusion s with killing or splitting rates related, respectively, to concave and con vex distortions. The main tools come from the theories of stochastic contro l, stochastic differential games, and non-linear partial differential equat ions. (C) 2000 Elsevier Science B.V. All rights reserved.