%0 Journal Article %T Non-concave utility maximisation on the positive real axis in discrete time %A Laurence Carassus %A Mikl¨®s R¨˘sonyi %A Andrea M. Rodrigues %J Quantitative Finance %D 2015 %I arXiv %X We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios. %U http://arxiv.org/abs/1501.03123v2