Optimal Credit Investment with Borrowing Costs

Forthcoming in Mathematics of Operations Research

36 Pages Posted: 26 Aug 2016

See all articles by Lijun Bo

Lijun Bo

University of Science and Technology of China (USTC)

Agostino Capponi

Columbia University - Department of Industrial Engineering and Operations Research

Date Written: August 25, 2016

Abstract

We consider the portfolio decision problem of a risky investor. The investor borrows at a rate higher than his lending rate, and invests in a risky bond whose market price is correlated with the credit quality of the investor. By viewing the concave drift of the wealth process as a continuous function of the admissible control, we characterize the optimal strategy in terms of a relation between a critical borrowing threshold and solutions of a system of first order conditions. We analyze the nonlinear dynamic programming equation and prove singular growth of its coefficients. Using a truncation technique relying on the locally Lipschitz-continuity of the optimal strategy, we remove the singularity and show existence and uniqueness of a global regular solution. Our explicit characterization of the strategy has direct financial implications: it indicates that the investor switches from overinvesting in the bond when his borrowing costs are low and the bond sufficiently safe to underinvesting or short-selling it when his financing costs are high or the bond very risky.

Keywords: borrowing costs, credit risk, optimal investment

JEL Classification: G11, G31, C61

Suggested Citation

Bo, Lijun and Capponi, Agostino, Optimal Credit Investment with Borrowing Costs (August 25, 2016). Forthcoming in Mathematics of Operations Research, Available at SSRN: https://ssrn.com/abstract=2829654

Lijun Bo

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

96, Jinzhai Road
Hefei, Anhui 230026
China

Agostino Capponi (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research ( email )

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