We study a sequence of many-agent exit time stochastic control problems, parameterized by the number of agents, with risk-sensitive cost structure. We identify a fully characterizing assumption, under which each such control problem corresponds to a risk-neutral stochastic control problem with additive cost, and sequentially to a risk-neutral stochastic control problem on the simplex that retains only the distribution of states of agents, while discarding further specific information about the state of each agent. Under some additional assumptions, we also prove that the sequence of value functions of these stochastic control problems converges to the value function of a deterministic control problem, which can be used for the design of nearly optimal controls for the original problem, when the number of agents is sufficiently large.

我们研究了一系列由风险敏感的成本结构决定的，由代理商数量参数化的多代理商退出时间随机控制问题。我们确定一个完全特征化的假设，在该假设下，每个此类控制问题都对应于具有附加成本的风险中立型随机控制问题，并依次对应于单纯形上仅保留主体状态分布的风险中立型随机控制问题，而丢弃有关每个代理状态的其他特定信息。在一些额外的假设下，我们还证明了这些随机控制问题的价值函数序列收敛于确定性控制问题的价值函数，该函数可用于设计原始问题的几乎最优控制。代理足够大。