Good deals in markets with friction
研究了在存在交易成本和风险度量下的投资策略优化问题，发现若定价规则不满足特定条件，投资者可获得风险收益接近理想值的好交易，且该问题在无摩擦模型中普遍存在。
This paper studies an optimization problem involving pay-offs of (perhaps dynamic) investment \nstrategies. The pay-off is the decision variable, the expected pay-off is maximized and its risk is \nminimized. The pricing rule may incorporate transaction costs and the risk measure is continuous, \ncoherent and expectation bounded.We will prove the necessity of dealing with pricing rules such that \nthere exists an essentially bounded stochastic discount factor that must also be bounded from below \nby a strictly positive value. Otherwise, good deals will be available to traders, i.e. depending on the \nselected risk measure, investors can choose pay-offs whose (risk, return) will be as close as desired \nto (−1,1) or (−1,1). This pathological property still holds for vector risk measures (i.e. if we \nminimize a vector-valued function whose components are risk measures). It is worth pointing out that, \nessentially, bounded stochastic discount factors are not usual in the financial literature. In particular, \nthe most famous frictionless, complete and arbitrage-free pricing models imply the existence of good \ndeals for every continuous, coherent and expectation bounded (scalar or vector) measure of risk, and \nthe incorporation of transaction costs will not guarantee the solution of this caveat