We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider’s information flow by using the theory of enlargement of filtrations and then obtain explicit logarithmic utility maximization results to compare optimal wealth for the insider and the ordinary agent.

中文翻译：

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与明显随机时间和最佳投资有关的信息不确定性

我们研究了违约风险下的最优投资问题，其中相关信息（如违约损失或恢复）被视为在违约时添加的外生随机标记。考虑具有不同信息级别的两种类型的代理。我们首先使用过滤的扩大理论来精确化内部人的信息流，然后获得明确的对数效用最大化结果，以比较内部人和普通代理人的最佳财富。