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We consider the problem of optimal portfolio selection under forwardinvestment performance criteria in an incomplete market. The dynamics of theprices of the traded assets depend on a pair of stochastic factors, namely, aslow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochasticvolatility). We analyze the associated forward performance SPDE and provideexplicit formulae for the leading order and first order correction terms forthe forward investment process and the optimal feedback portfolios. They bothdepend on the investor's initial preferences and the dynamically changinginvestment opportunities. The leading order terms resemble their time-monotonecounterparts, but with the appropriate stochastic time changes resulting fromaveraging phenomena. The first-order terms compile the reaction of the investorto both the changes in the market input and his recent performance. Ouranalysis is based on an expansion of the underlying ill-posed HJB equation, andit is justified by means of an appropriate remainder estimate.

Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations