Choice of financing mode as a stochastic bounded control problem

Miglo, Anton (2014): Choice of financing mode as a stochastic bounded control problem.

Abstract

In this note I analyze situations where an entrepreneur needs external financing from an outside investor in order to start an investment project that will yield a profit for two consecutive periods. The value of second-period profit is the entrepreneur's private information. I show that the choice of financing mode can be transformed into an optimal stochastic bounded control problem, where the state variable t represents the investor's first-period payoff and the control variable α can be interpreted in terms of the investor's residual profit rights. I then show that under certain general conditions such as the monotonicity and continuity of t (which have clear economic interpretations), an optimal contract is characterized by maximal α under low values of t and minimal α under high values of t. In economic terms this corresponds to debt.

• Item Type: MPRA Paper
• Language: English
• Keywords: optimal financing, stochastic optimization, bounded control, asymmetric information, debt
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C79 - Other; G - Financial Economics > G3 - Corporate Finance and Governance; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill

References

I. Cho and D. Kreps. Signalling games and Stable Equilibrium. Quarterly Journal of Economics. May, 102, 2, 179-121. 1987.

M. Dewatripont and J. Tirole. The Theory of Debt and Equity: Diversity of Securities and Manager-Shareholder Congruence. Quarterly Journal of Economics, 109, 1027-54. 1994

M. Harris and A. Raviv. The Design of Securities. Journal of Financial Economics, 24 (2), 255-288. 1989.

O. Hart. Firms, Contracts, and Financial Structure. Oxford University Press. 1995.

R. Innes. Limited Liability and Incentive Contracting with ex-ante Choices. Journal of Economic Theory, 52: 45-67. 1990.

I. Jewitt. Applications of Likelihood Ratio Orderings in Economics. In Misler, K. and Scarsini, M., editors. Stochastic Orders and Decisions under Risk, volume 19. Institute of Mathematical Statistics Lecture Notes. 1991.

M. Kamien and N. Scwartz. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, Series of Volumes in Dynamic Economics: Theory and applications, North-Holland.ed. M. Wilkinson. 1981.

A. Kolmogorov and S. Fomin. Introductory real analysis. Revised English Edition Translated and Edited by Richard A. Silverman. Dover publications, inc. New-York. 1970.

S. Matthews. Renegotiating Moral Hazard Contracts under Limited Liability and Monotonicity. Journal of Economic Theory, 97, 1-29. 2001.

F. Modigliani and M. Miller. The Cost of Capital, Corporation Finance, and the Theory of Investment. American Economic Review, 261-297. 1958.

S. Myers and N. Majluf. Corporate Financing and Investment Decisions When Firms Have Information That Investors Do not have. Journal of financial economics; 13(2), June, 187-221. 1984.

D. Nachman and T. H. Noe. Optimal Design of Securities under Asymmetric information. The Review of Financial Studies Spring 1994 Vol. 7 No. 1, 1-44. 1994.

E. Wolfstetter. Topics in Microeconomics. Cambridge University Press. 1999.