Stochastic Differential Games and Optimization Problems with Controlled Point Process Arrivals
本文研究受控跳跃强度的随机微分博弈，提出渐近马尔可夫均衡，并通过例子说明其与受控跳跃大小的博弈均衡相似，为相关优化问题提供解法。
Abstract There is a very large literature on applications of stochastic control of jump diffusions and a smaller literature on such games. In many applications it is natural to assume that the arrival intensity is controlled, but except for two long-forgotten papers the literature instead assumes that it is the jump sizes that are controlled. The more natural assumption is typically avoided because a failed Lipschitz condition means that the classical existence and uniqueness proofs cannot be used. We here derive an asymptotic Markov equilibrium of the game with controlled jump intensities and show that it, at least in an example, is very similar to the Markov equilibrium of an analog game with controlled jump sizes. The paper thus makes two contributions: It supplies a way to solve some optimization problems and games with controlled jump intensities and it shows that the commonly used formulation with controlled jump sizes is quite defensible for at least some classes of games.