Risk Sensitive Asset Management and Cascading Defaults

Forthcoming, Mathematics of Operations Research

35 Pages Posted: 20 Apr 2016 Last revised: 22 Feb 2017

See all articles by John R. Birge

John R. Birge

University of Chicago - Booth School of Business

Lijun Bo

University of Science and Technology of China (USTC)

Agostino Capponi

Columbia University

Date Written: February 21, 2017

Abstract

We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasi-linear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor accounts for contagion effects when making investment decisions, reduces his risk exposure as he becomes more sensitive to risk, and that his strategy depends non-monotonically on the aggregate risk level.

Keywords: risk-sensitive control, cascading defaults, contagion, asset management

JEL Classification: C32, C52, D81, D83, D84

Suggested Citation

Birge, John R. and Bo, Lijun and Capponi, Agostino, Risk Sensitive Asset Management and Cascading Defaults (February 21, 2017). Forthcoming, Mathematics of Operations Research. Available at SSRN: https://ssrn.com/abstract=2766387 or http://dx.doi.org/10.2139/ssrn.2766387

John R. Birge

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Lijun Bo

University of Science and Technology of China (USTC) ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Agostino Capponi (Contact Author)

Columbia University ( email )

S. W. Mudd Building
New York, NY 10027
United States

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