Information uncertainty related to marked random times and optimal investment

TL;DR

This paper investigates optimal investment strategies under default risk with exogenous loss or recovery information, comparing insiders with more information to ordinary agents using filtration theory.

Contribution

It introduces a model incorporating marked default times and explicitly compares insider and ordinary agent optimal wealth using filtration enlargement theory.

Findings

Explicit logarithmic utility maximization results

Insider's information leads to higher optimal wealth

Framework for analyzing information asymmetry in default risk

Abstract

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. MSC: 60G20, 91G40, 93E20