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Review of Quantitative Finance and Accounting
Published in:

11-12-2023 | Original Research

Optimal dividend decisions with capital infusion in a dynamic nonterminal bankruptcy model

Authors: Shu Zhang, Peimin Chen, Chunchi Wu

Published in: Review of Quantitative Finance and Accounting | Issue 3/2024

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Abstract

We develop a stochastic dynamic model of dividend optimization under the conditions of a positive recovery, in which shareholders can recover a portion of their capital, and nonterminal bankruptcy due to private capital infusion or government bailout. In the presence of a recovery, the optimization problem becomes a mixed classical impulse stochastic control problem. We provide a closed-form solution for optimal dividend payout and timing under nonterminal bankruptcy. We take the model to the real data and show that this model explains the dividend puzzle during the financial crisis when the US government bailed out insurance companies and banks.
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Appendix
Available only for authorised users
Footnotes
1
For example, a diffusion model with random returns has been considered in Sethi and Taksar (2002) for a company that can issue new equity when the surplus becomes negative. Along a similar line, Kulenko and Schimidli (2008), Yao et al. (2011) and Jin and Yin (2013) analyze the optimal dividend problem with capital injections and derive closed-form solutions.
 
2
For example, given the too-big-to-fail attitude held by the government, the government did not let big financial companies fail during the financial crisis because it can have huge consequences on the economy. While some monoline insurance companies and regional banks were allowed to bankrupt during the subprime crisis, they were liquidated with residual values distributed to stockholders.
 
3
The estimation of these parameters is discussed in Sect. 7. Here, \(1-k_0\) is the tax rate and \(K_0\) is the transaction cost of dividends.
 
4
In this and next section, the unit of dividend time we use is a day.
 
5
Paying dividends more quickly sends out a signal that firms have the ability to survive, thereby increasing the confidence of short-term creditors.
 
8
We normalize the scale of raw data to increase the precision of dividend time and amount estimates in empirical tests.
 
9
See bailout for Fannie Mae on website: https://​projects.​propublica.​org.
 
10
This is the last quarter in which bailout data are available and represents the best choice for estimating the implied cost of dividends.
 
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Metadata
Title
Optimal dividend decisions with capital infusion in a dynamic nonterminal bankruptcy model
Authors
Shu Zhang
Peimin Chen
Chunchi Wu
Publication date
11-12-2023
Publisher
Springer US
Published in
Review of Quantitative Finance and Accounting / Issue 3/2024
Print ISSN: 0924-865X
Electronic ISSN: 1573-7179
DOI
https://doi.org/10.1007/s11156-023-01229-1

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