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Computation of distorted probabilities for diffusion processes via stochastic control methods. (English) Zbl 1103.65305

Summary: 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.

MSC:

65C50 Other computational problems in probability (MSC2010)
60J60 Diffusion processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
91A15 Stochastic games, stochastic differential games
93E20 Optimal stochastic control
91B30 Risk theory, insurance (MSC2010)
91B26 Auctions, bargaining, bidding and selling, and other market models
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