Advances in Applied Probability

Optimal financing and dividend distribution in a general diffusion model with regime switching

Jinxia Zhu and Hailiang Yang

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Abstract

We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model, where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both capital injection and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of the capital injection. We prove that it is optimal to inject capital only when the surplus tends to fall below 0 and to pay out dividends at the maximal rate when the surplus is at or above the threshold, dependent on the environment regime.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 2 (2016), 406-422.

Dates
First available in Project Euclid: 9 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1465490755

Mathematical Reviews number (MathSciNet)
MR3511768

Zentralblatt MATH identifier
1343.49032

Subjects
Primary: 49L20: Dynamic programming method
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Keywords
Dividend general diffusion optimization optimal financing regime-switching

Citation

Zhu, Jinxia; Yang, Hailiang. Optimal financing and dividend distribution in a general diffusion model with regime switching. Adv. in Appl. Probab. 48 (2016), no. 2, 406--422. https://projecteuclid.org/euclid.aap/1465490755


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References

  • Bäuerle, N. (2004). Approximation of optimal reinsurance and dividend payout policies. Math. Finance 14, 99–113.
  • Cadenillas, A., Sarkar, S. and Zapatero, F. (2007). Optimal dividend policy with mean-reverting cash reservoir. Math. Finance 17, 81–109.
  • Dickson, D. C. M. and Waters, H. R. (2004). Some optimal dividends problems. ASTIN Bull. 34, 49–74.
  • Fleming, W. H. and Soner, H. M. (1993). Controlled Markov Processes and Viscosity Solutions (Appl. Math. (New York) 25.) Springer, New York.
  • He, L. and Liang, Z. (2008). Optimal financing and dividend control of the insurance company with proportional reinsurance policy. Insurance Math. Econom. 42, 976–983.
  • Højgaard, B. and Taksar, M. (2001). Optimal risk control for a large corporation in the presence of returns on investments. Finance Stoch. 5, 527–547.
  • Ikeda, N. and Watanabe, S. (1977). A comparison theorem for solutions of stochastic differential equations and its applications. Osaka J. Math. 14, 619–633.
  • Jiang, Z. and Pistorius, M. (2012). Optimal dividend distribution under Markov regime switching. Finance Stoch. 16, 449–476.
  • Krylov, N. V. (1996). Lectures on Elliptic and Parabolic Equations in Hölder Spaces. American Mathematical Society, Providence, RI.
  • Løkka, A. and Zervos, M. (2008). Optimal dividend and issuance of equity policies in the presence of proportional costs. Insurance Math. Econom. 42, 954–961.
  • Paulsen, J. (2008). Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs. SIAM J. Control Optimization 47, 2201–2226.
  • Scheer, N. and Schmidli, H. (2011). Optimal dividend strategies in a Cramér–Lundberg model with capital injections and administration costs. Europ. Actuarial J. 1, 57–92.
  • Shreve, S. E., Lehoczky, J. P. and Gaver, D. P. (1984). Optimal consumption for general diffusions with absorbing and reflecting barriers. SIAM J. Control Optimization 22, 55–75.
  • Sotomayor, L. R. and Cadenillas, A. (2011). Classical and singular stochastic control for the optimal dividend policy when there is regime switching. Insurance Math. Econom. 48, 344–354.
  • Taksar, M. I. (2000). Optimal risk and dividend distribution control models for an insurance company. Math. Meth. Operat. Res. 51, 1–42.
  • Yao, D., Yang, H. and Wang, R. (2011). Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs. Europ. J. Operat. Res. 211, 568–576.
  • Zhu, J. (2014). Dividend optimization for a regime-switching diffusion model with restricted dividend rates. ASTIN Bull. 44, 459–494.
  • Zhu, J. (2015). Dividend optimization for general diffusions with restricted dividend payment rates. Scand. Actuarial J. 2015, 592–615.
  • Zhu, J. and Yang, H. (2015). Optimal financing and dividend distribution in a general diffusion model with regime switching. Available at http://arxiv.org/abs/1506.08360.