# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020003

## On correlated defaults and incomplete information

 1 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 2 Corresponding author. Department of Mathematics, Southern University of Science and Technology, Shenzhen, China 3 Department of Mathematics, Imperial College, London, SW7 2AZ, UK

Received  June 2018 Revised  July 2019 Published  January 2020

In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value reports. In this situation, the default time of each firm becomes a totally inaccessible stopping time to the market participants. The original structural model is first transformed to a reduced-form model. Then the conditional distribution of the default time together with the asset value of each name are derived. We prove the existence of the intensity processes of default times and also give the explicit form of the intensity processes. Numerical studies on the intensities of the two correlated names are conducted for some special cases.

Citation: Wai-Ki Ching, Jia-Wen Gu, Harry Zheng. On correlated defaults and incomplete information. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020003
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##### References:
Default Intensity process $\lambda_2$ when $\tau_1 = 2$
Default Intensities of firm B where $\rho = -0.5$
Default Intensity Process $\lambda_2$ when $\rho = 0$
Default Intensity Process $\lambda_2$ when $\tau_1 = 2$ and $\rho = 0.1$
Default Intensity Process $\lambda_2$ when $\tau_1 = 2$ and $\rho = -0.1$
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