Non linear estimation of returns on hedge funds with scarce observations

Explaining the behavior of a financial portfolio like a Hedge Fund is challenging for many reasons, one of those reasons is scarce observations.  One possibility to circumvent these issues is to find simple relationships between the portfolio and financial factors.  These factors are observed more frequently so it is valid to assume that one can estimate not only the conditional expectation with respect to single factors, but also the joint law of all the underlying factors.  The problem, then, is to recover the conditional expectation of the portfolio’s return given all the factors.The author of the paper,”Measuring Risk With Scarce Observation” prescribes a reasonable criteria which provides existence and uniqueness to this problem also characterizes  the  solution  under  the  assumption  of  Gaussian  distribution  among the factors (Independent factors).  In our thesis, we present a solution for the casewhen the joint law of factors is a multivariate t-student distribution.