Optimal Investment and Debt Repayment with Transaction Costs under a HJB Framework in Incomplete Markets: A Numerical Study

Author(s)	Mr. Mwanda Bumali, Dr. Joseph Eyang'an Esekon, Dr. Richard Otieno Opiyo
Country	Kenya
Abstract	This paper analyses four stochastic control models for optimal investment and debt management in an incomplete market, progressing from a frictionless benchmark to a full model incorporating proportional transaction costs and mandatory debt amortization. We solve each model using the Hamilton-Jacobi-Bellman framework and quasi-variational inequalities, deriving closed-form value functions and optimal policies. Major findings show that mandatory amortization asymmetrically tightens the no-trade region, forcing earlier deleveraging, while transaction costs widen the inaction zone. Numerical experiments confirm convergence and accuracy. Practically, these results imply that firms with debt obligations cannot afford passive portfolio strategies; they must rebalance more actively than frictionless models suggest, especially as debt repayment deadlines approach.
Keywords	Transaction costs, Debt amortization, Incomplete markets, Hamilton–Jacobi–Bellman equation, Quasi-variational inequality
Field	Mathematics
Published In	Volume 8, Issue 3, May-June 2026
Published On	2026-06-06
DOI	https://doi.org/10.36948/ijfmr.2026.v08i03.80308

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