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Modeling the Dependency Structure of Integrated Intensity Processes.
1Department of Applied Mathematics, Kongju National University, Gongju-si, Chungcheongnam-do, Republic of Korea.
Plos One
|August 14, 2015
Summary
This study models dependence structures using Cox processes driven by correlated shot noise. The findings guide credit risk management by analyzing joint intensity probabilities.
Area of Science:
- Financial Mathematics
- Stochastic Processes
- Risk Management
Background:
- Modeling dependence structures is crucial in financial mathematics.
- Cox processes are widely used for event modeling.
- Shot noise processes introduce jumps and variability.
Purpose of the Study:
- To develop a model for dependence structures in Cox processes.
- To analyze the impact of correlated shot noise on intensity processes.
- To provide insights for credit risk management.
Main Methods:
- Utilizing dependent shot noise processes to drive Cox process intensities.
- Modeling simultaneous jumps and correlated jump sizes.
- Deriving the joint survival probability of integrated intensities using copulas with exponential marginal distributions.
Main Results:
- Explicitly obtained the joint survival probability of integrated intensities.
- Demonstrated the application of the copula-based approach.
- Established a link between stochastic modeling and financial applications.
Conclusions:
- The developed model effectively captures dependence structures.
- The explicit joint survival probability is a valuable tool.
- The results offer practical guidance for credit risk management.
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