实现可接受性的资本要求
Capital Requirement for Achieving Acceptability
摘要：
考虑一个在t = 0日进入金融市场的代理人，初始资本金额为x。他把这笔钱投资在股票和货币市场上，到t = T时，他已经产生了财富W。他给出了一个凸类的概率测度（称为场景）和一个实值函数（或地板）对应于每个场景。代理人面临的约束条件是，在每个场景下的期望W不得小于相应的地板。我们称x是可接受的，如果我们可以从x开始并成功地生成满足这些约束的W。可接受x的集合是R中的半直线，从上到下是无界的。我们表明，在一定的规则性条件下的情况下，该集的下确界的地板上确界的所有情况下，S是一个鞅。
英文摘要：
Consider an agent who enters a financial market on day t = 0 with an initial capital amount x. He invests this amount on stocks and the money market, and by day t = T, has generated a wealth W . He is given a convex class of probability measures (called scenarios) and a real-valued function (or floors) corresponding to each scenario. The agent faces the constraints that the expectation of W under each scenario must not be less than the corresponding floor. We call x acceptable if one can start with x and successfully generate W satisfying these constraints. The set of acceptable x is a half-line in R, unbounded from above. We show that under some regularity conditions on the set of scenarios and the floor function, the infimum of this set is given by the supremum of the floors over all scenarios under which S is a martingale.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
