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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Davis BE (1970) Investment and rate of return for the regulated firm. Bell J Econ Manag Sci 1:245–270
Davis BE, Elzinga DJ (1971) The solution of an optimal control problem in financial modeling. Oper Res 19:1419–1433
Elton E, Gruber M (1975) Finance as a dynamic process. Prentice-Hall, Englewood Cliffs
Gordon MJ (1962) The investment, financing and valuation of the corporation. Richard D. Irwin, Homewood
Isaacs R (1965) Differential games. Wiley, New York
Krouse CG (1972) Optimal financing and capital structure programs for the firm. J Financ 27:1057–1071
Krouse CG, Lee WY (1973) Optimal equity financing of the corporation. J Financ Quant Anal 8:539–563
Miller MH, Modigliani F (1961) Dividend policy, growth, and valuation of shares. J Bus 34:411–433
Perrakis S (1976) A note on optimal equity financing of the corporation. J Financ Quant Anal 11(1):157–164
Sethi SP (1973d) A note on modeling simple dynamic cash balance problems. J Financ Quant Anal 8:685–687; Errata, 13, 585–586
Sethi SP (1978b) Optimal equity financing model of Krouse and Lee: corrections and extensions. J Financ Quant Anal 13(3):487–505
Sethi SP (1996) When does the share price equal the present value of future dividends? - a modified dividend approach. Econ Theory 8:307–319
Sethi SP, Thompson GL (1970) Applications of mathematical control theory to finance. J Financ Quant Anal 5(4–5):381–394
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Sethi, S.P. (2021). Applications to Finance . In: Optimal Control Theory. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-91745-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-91745-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-91744-9
Online ISBN: 978-3-030-91745-6
eBook Packages: Business and ManagementBusiness and Management (R0)