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Applications to Finance Applications to finance

In: Optimal Control Theory

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  • Suresh P. Sethi

    (University of Texas at Dallas)

Abstract

An important area of finance involves making decisions regarding investment and dividend policies over time and ways to finance them. Among the ways of financing are issuing equity, retaining earnings, and borrowing money. This chapter deal with two different problems relating to a firm. Section 5.1 treats a cash balance problem, which in its simplest form, is a problem of controlling the level of a firm’s cash balances to meet its demand for cash at the minimum total cost. The problem is solved explicitly using the maximum principle. Section 5.2 deals with the optimal equity financing of a corporate firm by determining the optimal dividend path along with new equity issued over time to maximize the value of the firm. To obtain the optimal path, we synthesize an optimal sequence of subcases, obtained using the maximum principle, by employing a switching-point analysis based on a reverse-time construction technique. Moreover and importantly, the chapter provides financial interpretations for the various functions such as the Hamiltonian and the adjoint functions that arise in the course of the analysis. There are many exercises at the end of the chapter.

Suggested Citation

  • Suresh P. Sethi, 2021. "Applications to Finance Applications to finance," Springer Texts in Business and Economics, in: Optimal Control Theory, edition 4, chapter 5, pages 145-174, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-91745-6_5
    DOI: 10.1007/978-3-030-91745-6_5
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