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Finance and Stochastics

, Volume 19, Issue 4, pp 891–939 | Cite as

Dynamic credit investment in partially observed markets

  • Agostino Capponi
  • José E. Figueroa-López
  • Andrea Pascucci
Article

Abstract

We consider the problem of maximizing the expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous-time finite-state Markov chain. We reduce the partially observed stochastic control problem to a complete observation risk-sensitive control problem via the filtered regime switching probabilities. We separate the latter into predefault and postdefault dynamic optimization subproblems and obtain two coupled Hamilton–Jacobi–Bellman (HJB) partial differential equations. We prove the existence and uniqueness of a globally bounded classical solution to each HJB equation and give the corresponding verification theorem. We provide a numerical analysis showing that the investor increases his holdings in stock as the filter probability of being in high-growth regimes increases, and decreases his credit risk exposure as the filter probability of being in high default risk regimes gets larger.

Keywords

Partial information Filtering Risk-sensitive control Default risk Hidden Markov chain 

Mathematics Subject Classification (2010)

93E20 91G10 49L20 93E11 

JEL Classification

G11 C61 C11 

Notes

Acknowledgements

The authors gratefully acknowledge two anonymous reviewers and Wolfgang Runggaldier for providing constructive and insightful comments, which improved significantly the quality of the manuscript. Agostino Capponi would also like to thank Ramon van Handel for very useful discussions and insights provided in the original model setup.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Agostino Capponi
    • 1
  • José E. Figueroa-López
    • 2
  • Andrea Pascucci
    • 3
  1. 1.Industrial Engineering and Operations Research DepartmentColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsWashington UniversitySt. LouisUSA
  3. 3.Department of MathematicsUniversity of BolognaBolognaItaly

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