基于随机网络优化的股票市场交易
Stock Market Trading Via Stochastic Network Optimization
摘要：
我们考虑的问题的动态购买和出售的股票从一个集合的$N$股票的随机价格波动。为了限制投资风险，我们对任何时候持有的股票总数设定了上限。假设价格按照具有轻微衰减记忆特性的各态历经过程演化，并假设在任何时候可以买卖的股票总数受到限制，我们开发出一种交易策略，它任意地接近于实现对未来事件具有完美知识的理想策略的利润。接近最优利润伴随着最大所需库存水平和与收敛相关的时间尺度的相应权衡。然后，我们考虑任意（可能是非遍历）的价格过程，并表明，相同的算法接近利润的帧为基础的政策，可以期待一个固定数量的插槽到未来。我们的分析使用了我们最初为随机网络优化问题开发的Lyapunov优化技术。
英文摘要：
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that prices evolve according to an ergodic process with a mild decaying memory property, and assuming constraints on the total number of shares that can be bought and sold at any time, we develop a trading policy that comes arbitrarily close to achieving the profit of an ideal policy that has perfect knowledge of future events. Proximity to the optimal profit comes with a corresponding tradeoff in the maximum required stock level and in the timescales associated with convergence. We then consider arbitrary (possibly non-ergodic) price processes, and show that the same algorithm comes close to the profit of a frame based policy that can look a fixed number of slots into the future. Our analysis uses techniques of Lyapunov Optimization that we originally developed for stochastic network optimization problems.
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