Balbás, AlejandroBalbás, BeatrizBalbás, Raquel2014-01-202015-01-012013-06Quantitative Finance, vol. 13, no. 6, pp. 827-8361469-7688https://hdl.handle.net/10016/18157This paper studies an optimization problem involving pay-offs of (perhaps dynamic) investment strategies. The pay-off is the decision variable, the expected pay-off is maximized and its risk is minimized. The pricing rule may incorporate transaction costs and the risk measure is continuous, coherent and expectation bounded.We will prove the necessity of dealing with pricing rules such that there exists an essentially bounded stochastic discount factor that must also be bounded from below by a strictly positive value. Otherwise, good deals will be available to traders, i.e. depending on the selected risk measure, investors can choose pay-offs whose (risk, return) will be as close as desired to (−1,1) or (−1,1). This pathological property still holds for vector risk measures (i.e. if we minimize a vector-valued function whose components are risk measures). It is worth pointing out that, essentially, bounded stochastic discount factors are not usual in the financial literature. In particular, the most famous frictionless, complete and arbitrage-free pricing models imply the existence of good deals for every continuous, coherent and expectation bounded (scalar or vector) measure of risk, and the incorporation of transaction costs will not guarantee the solution of this caveatapplication/pdfengTaylor & FrancisRisk measuresTransaction costsPortfolio optimizationArbitrage relationshipresearch articleG1G11G12G1310.1080/14697688.2013.780132open access8276836Quantitative Finance13AR/0000013496