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The most commonly accepted model for investors' preferences is expectedutility theory. More recently, other theories have emerged and pose newchallenges to mathematics. The present paper treats preferences of cumulativeprospect theory (CPT), where an "S-shaped" utility function is considered (i.e.convex up to a certain point and concave from there on). Also, distortedprobability measures are applied for calculating the utility of a givenposition with respect to a (possibly random) benchmark $G$. Such problems haveheretofore been solved essentially for complete continuous-time market modelsonly. In the present paper we make a step forward and consider incompletemodels of a diffusion type where the return of the investment in considerationdepends on some economic factors. Our main result asserts, under mildassumptions, the existence of an optimal strategy when the driving noise of theeconomic factors is independent of that of the investment and the rate ofreturn is non-negative. We are also able to accommodate models of a specifictype where the factor may have non-zero correlation with the investment.

Optimal investment under behavioural criteria in incomplete diffusion market models