英文标题：
《Optimal Real-Time Bidding Strategies》
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作者：
Joaquin Fernandez-Tapia, Olivier Gu\\\'eant, Jean-Michel Lasry
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最新提交年份：
2016
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英文摘要：
The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (KPI). The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the \\textit{price to beat} for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and that almost-closed form solutions can be found by using a fluid limit. Numerical examples are also carried out.
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中文摘要：
媒体购买机构的广告交易台越来越依赖复杂的算法来购买广告库存。特别是，实时竞价（RTB）算法在一天中响应许多拍卖——通常是Vickrey拍卖——以购买广告库存，目的是最大化一个或多个关键性能指标（KPI）。对于应用数学家群体来说，制定投标策略的公司所面临的优化问题是新的、有趣的。在本文中，我们引入了一个随机最优控制模型，该模型解决了各种现实情况下的最优竞价策略问题：在受众策略的框架下，以给定数量的现金购买的库存最大化，以给定数量的现金购买/转换的数量最大化，等等。在我们的模型中，拍卖序列由泊松过程建模，每次拍卖的{price to beat}由遵循几乎任何概率分布的随机变量建模。我们证明了最优投标由Hamilton-Jacobi-Bellman方程描述，并且通过使用流体极限可以找到几乎封闭形式的解。并给出了数值算例。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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