英文标题：
《Nonzero-sum stochastic differential games with impulse controls: a
verification theorem with applications》
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作者：
Ren\\\'e A\\\"id, Matteo Basei, Giorgia Callegaro, Luciano Campi, Tiziano
Vargiolu
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最新提交年份：
2018
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英文摘要：
We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the value functions and the optimal strategies of the two players. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric running payoffs. We fully characterize a Nash equilibrium and provide explicit expressions for the optimal strategies and the value functions. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further non-symmetric examples where a Nash equilibrium is found numerically.
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中文摘要：
我们考虑一个一般的两人非零和脉冲博弈。本文的主要数学贡献是一个验证定理，它在某些正则条件下，为两个参与者的值函数和最优策略提供了一个合适的拟变分不等式组。作为一个应用，我们研究了一个一维状态变量的脉冲博弈，它遵循一个实值的标度布朗运动，以及两个具有线性和对称运行收益的博弈者。我们充分刻画了纳什均衡，并给出了最优策略和价值函数的显式表达式。我们还证明了关于干预成本的一些渐近结果。最后，我们考虑另外两个非对称的例子，其中一个纳什均衡在数值上被发现。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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