A parallel algorithm for optimizing the capital structure contingent on maximum value at risk.

Purpose – The purpose of this paper is to measure the financial risk and optimal capital structure of a corporation. Design/methodology/approach – Irregular disjunctive programming problems arising in firm models and risk management can be solved by the techniques presented in the paper. Findings – Parallel processing and mathematical modeling provide a fruitful basis for solving ultra-scale non-convex general disjunctive programming (GDP) problems, where the computational challenge in direct mixed-integer non-linear programming (MINLP) formulations or single processor algorithms would be insurmountable. Research limitations/implications – The test is limited to a single firm in an experimental setting. Repeating the test on large sample of firms in future research will indicate the general validity of Monte-Carlo-based VAR estimation. Practical implications – The authors show that the risk surface of the firm can be approximated by integrated use of accounting logic, corporate finance, mathematical programming, stochastic simulation and parallel processing. Originality/value – Parallel processing has potential to simplify large-scale MINLP and GDP problems with non-convex, multi-modal and discontinuous parameter generating functions and to solve them faster and more reliably than conventional approaches on single processors