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In this article, we consider the problem of a bank's loan portfolio in thecontext of liquidity risk, while allowing for the limited liability protectionenjoyed by the bank. Accordingly, we construct a novel loan portfolio modelwith limited liability, while maintaining a threshold level of haircut in theportfolio. For the constructed three-time step loan portfolio, at the initialtime, the bank raises capital via debt and equity, investing the same inseveral classes of loans, while at the final time, the bank either meets itsliabilities or becomes insolvent. At the intermediate time step, a fraction ofthe deposits are withdrawn, resulting in liquidation of some of the bank'sassets. The liquidated portfolio is designed with the goal of minimizing theliquidation cost. Our theoretical results show that model with the haircutconstraint leads to lesser liquidity risk, as compared to the scenario of nohaircut constraint being imposed. Finally, we present numerical results toillustrate the theoretical results which were obtained.

Loan portfolio management and Liquidity Risk: The impact of limited liability and haircut