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

Ralf Östermark (School of Business and Economics, Åbo Akademi University, Turku, Finland)


ISSN: 0368-492X

Article publication date: 2 March 2015




The purpose of this paper is to measure the financial risk and optimal capital structure of a corporation.


Irregular disjunctive programming problems arising in firm models and risk management can be solved by the techniques presented in the paper.


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.


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.



Östermark, R. (2015), "A parallel algorithm for optimizing the capital structure contingent on maximum value at risk", Kybernetes, Vol. 44 No. 3, pp. 384-405.



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