英文标题：
《Adaptive Pricing in Insurance: Generalized Linear Models and Gaussian
  Process Regression Approaches》
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作者：
Yuqing Zhang and Neil Walton
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最新提交年份：
2019
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英文摘要：
  We study the application of dynamic pricing to insurance. We view this as an online revenue management problem where the insurance company looks to set prices to optimize the long-run revenue from selling a new insurance product. We develop two pricing models: an adaptive Generalized Linear Model (GLM) and an adaptive Gaussian Process (GP) regression model. Both balance between exploration, where we choose prices in order to learn the distribution of demands & claims for the insurance product, and exploitation, where we myopically choose the best price from the information gathered so far. The performance of the pricing policies is measured in terms of regret: the expected revenue loss caused by not using the optimal price. As is commonplace in insurance, we model demand and claims by GLMs. In our adaptive GLM design, we use the maximum quasi-likelihood estimation (MQLE) to estimate the unknown parameters. We show that, if prices are chosen with suitably decreasing variability, the MQLE parameters eventually exist and converge to the correct values, which in turn implies that the sequence of chosen prices will also converge to the optimal price. In the adaptive GP regression model, we sample demand and claims from Gaussian Processes and then choose selling prices by the upper confidence bound rule. We also analyze these GLM and GP pricing algorithms with delayed claims. Although similar results exist in other domains, this is among the first works to consider dynamic pricing problems in the field of insurance. We also believe this is the first work to consider Gaussian Process regression in the context of insurance pricing. These initial findings suggest that online machine learning algorithms could be a fruitful area of future investigation and application in insurance.
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中文摘要：
我们研究了动态定价在保险中的应用。我们认为这是一个在线收入管理问题，保险公司希望通过设定价格来优化销售新保险产品的长期收入。我们开发了两种定价模型：自适应广义线性模型（GLM）和自适应高斯过程（GP）回归模型。两者都在探索和开发之间取得平衡，在探索中，我们选择价格，以了解保险产品的需求和索赔的分布情况；在开发中，我们从迄今为止收集的信息中，目光短浅地选择最佳价格。定价政策的绩效以遗憾来衡量：未使用最优价格造成的预期收入损失。正如保险业中常见的情况一样，我们通过GLMs对需求和索赔进行建模。在我们的自适应GLM设计中，我们使用最大拟似然估计（MQLE）来估计未知参数。我们表明，如果价格的可变性适当降低，MQLE参数最终会存在并收敛到正确的值，这反过来意味着所选价格的序列也会收敛到最优价格。在自适应GP回归模型中，我们从高斯过程中采样需求和索赔，然后根据置信上限规则选择销售价格。我们还分析了这些具有延迟索赔的GLM和GP定价算法。虽然在其他领域也存在类似的结果，但这是第一批考虑保险领域动态定价问题的工作。我们还认为，这是首次在保险定价的背景下考虑高斯过程回归。这些初步发现表明，在线机器学习算法可能是未来保险研究和应用的一个富有成效的领域。
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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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：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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