Skip to main content
SpringerLink
Log in

Stochastic Finance of a Company Associated with Ruin, Restricted Reserve, Dividends and Dividend Strategy

  • Research Article
  • Published:
Journal of the Indian Society for Probability and Statistics Aims and scope Submit manuscript

Abstract

In this paper a dual model of classical risk theory is considered to study the expected value of discounted dividends using imbedding method. The optimal dividend strategy is obtained in different forms. By the same technique the classical model is also analyzed. Further in the dual model expenses of a company are taken as proportional to the surplus to obtain optimal barrier strategy. We also consider a model with two components of incomes to the company in analyzing the optimal dividend strategy. In the dual model jump-diffusion is also introduced to determine the two components of dividends due to jump-gains and jump-diffusion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Albrecher H, Thonhauser S (2009) Optimality results for dividend problems in insurance. RACSAM Revista de la Real Acamedia de Ciencias Exactas Fisicas of Naturals Serie A Matematicas 103(2):295–320

    MathSciNet  MATH  Google Scholar 

  • Albrecher H, Thonhauser S (2011) The optimal dividend barrier with gamma–omega model. Eur Actuar J 1(1):43–55

    Article  MathSciNet  Google Scholar 

  • Albrecher H, Bäuerle N, Thonhauser S (2011) Optimal dividend-payout in random discrete time. Stat Risk Model 28(3):251–276

    Article  MathSciNet  MATH  Google Scholar 

  • Asmussen S, Taksar M (1997) Controlled diffusion models for optimal dividend pay-out. Insur Math Econ 20(1):1–15

    Article  MathSciNet  MATH  Google Scholar 

  • Asmussen S, Højgaard B, Taksar M (2000) Optimal risk control and dividend distribution policies. Examples of excess-of loss reinsurance for an insurance corporation. Finance Stoch 4(3):299–324

    Article  MathSciNet  MATH  Google Scholar 

  • Avanzi B (2009) Strategies for dividends distribution: a review. N Am Actuar J 13(2):217–251

    Article  MathSciNet  Google Scholar 

  • Avanzi B, Gerber H, Shiu E (2007) Optimal dividends in the dual model. Insur Math Econ 41(1):111–123

    Article  MathSciNet  MATH  Google Scholar 

  • Avanzi B, Cheung E, Wang B, Woo J (2013) On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency. Insur Math Econ 52(1):98–113

    Article  MathSciNet  MATH  Google Scholar 

  • Avanzi B, Tu V, Wang B (2014) On optimal periodic dividend strategies in the dual model with diffusion. Insur Math Econ 52(1):98–113

    Article  MathSciNet  Google Scholar 

  • Bai L, Paulsen J (2010) Optimal dividend policies with transaction costs for a class of diffusion processes. SIAM J Control Optim 48(8):4987–5008

    Article  MathSciNet  MATH  Google Scholar 

  • Bellman R, Wing M (1976) An introduction to invariant imbedding. Academic Press, New York

    MATH  Google Scholar 

  • Chen X, Xiao T, Yong X (2014) A Markov-modulated jump-diffusion risk model with randomized observation periods and threshold dividend strategy. Insur Math Econ 54:76–83

    Article  MathSciNet  MATH  Google Scholar 

  • Choulli T, Taksar M, Zhou X (2003) A diffusion model for optimal dividend distribution for a company with constraints on risk control. SIAM J Control Optim 41(6):1946–1979

    Article  MathSciNet  MATH  Google Scholar 

  • Cox D, Miller H (1965) The theory of stochastic processes. Chapman and Hall, London

    MATH  Google Scholar 

  • de Finetti B (1957) Siun impostazione alternativa della teoria collectiva del rischio. In: Transactions of XVth International Congress of Acturies, vol 2, pp 433–444

  • Dickson D, Waters H (2004) Some optimal dividend problems. ASTIN Bull 34:49–74

    Article  MathSciNet  MATH  Google Scholar 

  • Fang Y, Wu R (2007) Optimal dividend strategy in the compound poisson model with constant interest. Stoch Models 23(1):149–166

    Article  MathSciNet  MATH  Google Scholar 

  • Gerber H, Shiu E (2004) Optimal dividends: analysis with Brownian motion. N Am Actuar J 8(1):1–20

    Article  MathSciNet  MATH  Google Scholar 

  • Gerber H, Shiu E (2006) On optimal dividend strategies in the compound Poisson model. N Am Actuar J 10(2):76–93

    Article  MathSciNet  Google Scholar 

  • Hunting M, Paulsen J (2013) Optimal dividend policies with transaction costs for a class of jump-diffusion processes. Finance Stoch 17(1):73–106

    Article  MathSciNet  MATH  Google Scholar 

  • Jeanblanc-Picqué M, Shiryaev A (1995) Optimization of the flow of dividends. Russ Math Surv 50(2):257–277

    Article  MathSciNet  MATH  Google Scholar 

  • Liang Z, Young V (2012) Dividends and reinsurance under a penalty for ruin. Insur Math Econ 50(3):437–445

    Article  MATH  Google Scholar 

  • Liu X, Chen Z (2014) Dividend problems in the dual model with diffusion and exponentially distributed observation time. Stat Probab Lett 87:175–183

  • Lundberg F (1903) Approximerad framställning av Kollektiurisker. Almquist & Weksee, Stockholm

    Google Scholar 

  • Paulsen J (2008) Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportion cost. SIAM J Control Optim 47(5):2201–2226

    Article  MathSciNet  MATH  Google Scholar 

  • Peng D, Liu D, Liu Z (2008) Dividend problems in the dual risk model with exponentially distributed observation time. Stat Probab Lett 83(3):2201–2226

    MathSciNet  Google Scholar 

  • Schmidli H (2002) On minimizing the ruin probability by investment and reinsurance. Ann Appl Probab 12(3):890–907

    Article  MathSciNet  MATH  Google Scholar 

  • Slater L (1960) Confluent hypergeometric functions. Cambridge University Press, London

    MATH  Google Scholar 

  • Vittal PR, Vasudevan R (1987) Some first passage time problems with restricted reserve and two components of income. Scand Actuar J 1987(3–4):198–210

    Article  MathSciNet  MATH  Google Scholar 

  • Vittal PR, Jagadesan T, Muralidhar V (2008) Stochastic dynamics and passage times to diffusion approximations. Differ Equ Dyn Syst 16:145–163

    Article  MathSciNet  MATH  Google Scholar 

  • Vittal PR, Sakthivel K, Muralidhar V (2010) Expected overflow in a finite dam model for a class of master equations with separable kernels. Int J Stat Manag Syst 5:141–153

    Google Scholar 

  • Vittal PR, Thangaraj V, Muralidhar V (2011) Stochastic models for the amount of overflow in a finite dam with random inputs, random outputs and exponential release policy. Stoch Anal Appl 29(3):473–489

    Article  MathSciNet  MATH  Google Scholar 

  • Vittal PR, Thangaraj V, Muralidhar V (2013) Stochastic dynamics for passage times and diffusion approximation for finite capacity storage models with different kinds of barriers. Stoch Anal Appl 31(4):574–589

    Article  MathSciNet  MATH  Google Scholar 

  • Wang C, Liu X (2014) Dividend problems in the diffusion model with interest and exponentially distributed observation time. J Appl Prob Article ID 814835:1–6

  • Wei JQ, Wang RM, Yang H (2012) On the optimal dividend strategy in a regime-switching diffusion model. Adv Appl Probab 44(3):886–906

    Article  MathSciNet  MATH  Google Scholar 

  • Yu W, Huang Y (2011) Dividend payments and related problems in a Markov-dependent insurance risk model under absolute ruin. AJIBM 1:1–9

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Madras, Chepauk, Chennai, India

    P. R. Vittal

  2. Department of Mathematics, Vel Tech University, Chennai, India

    V. Thangaraj

  3. Department of Mathematics, Queen Mary’s College, Chennai, India

    S. Najeema

Authors
  1. P. R. Vittal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Thangaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Najeema
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. R. Vittal.

Additional information

A part of the work by P. R. Vittal was done while visiting Indian Statistical Institute, Bangalore. The first author acknowledges the support given by ISI Bangalore. The author acknowledges the encouragement given by Professors N. S. N. Sastry, Rajarama Bhat and Rajeev of Stat. Math. Unit, ISI Bangalore.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vittal, P.R., Thangaraj, V. & Najeema, S. Stochastic Finance of a Company Associated with Ruin, Restricted Reserve, Dividends and Dividend Strategy. J Indian Soc Probab Stat 17, 125–144 (2016). https://doi.org/10.1007/s41096-016-0009-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41096-016-0009-1

Keywords

Mathematics Subject Classification

Search

Navigation