Optimal dividends and capital injections strategy in a Markov-modulated risk model with restricted densities

Abstract

Keywords:
• Markov-modulated risk model stochastic control,
• HJB equation,
• capital injection strategy,
• dividend strategy

References

1. [1]

   BAUERLE N.Some results about the expected ruin time in Markov-modulated risk models[J].Insurance:Mathematics and Economics,1996,18:119.

2. [2]

   LU Y,LI S.On the probability of ruin in a Markov-modulated risk model[J].Insurance:Mathematics and Economics,2005,37(3):522.

3. [3]

   ZHANG X.On the ruin problem in a Markov-modulated risk model[J].Methodology and Computing in Applied Probability,2008,10(2):225.

4. [4]

   ZHU J,YANG H.Ruin probabilities of a dual Markov-modulated risk model[J].Communications in Statistics-Theory and Methods,2008,37(20):3298.

5. [5]

   LU Y,TSAI C C L.The expected discounted penalty at ruin for a Markov-modulated risk process perturbed by diffusion[J].North American Actuarial Journal,2007,11(2):136.

6. [6]

   WEI J,YANG H,WANG R.On the Markov-modulated insurance risk model with tax[J].Blätter der DGVFM,2010,31(1):65.

7. [7]

   KÖTTER M,BÄUERLE N.The Markov-modulated Risk Model with Investment[M].Springer Berlin Heidelberg,2007:575.

8. [8]

   LI S P,BAI Z W,MA C Y,et al.Markov modulated risk model with alternative premium rate[J].Journal of Systems Engineering,2011,26(6):752.

9. [9]

   LI S,LU Y.Some optimal dividend problems in a markov-modulated risk model[J].Insurance Mathematics and Economics,2006,39(3):423.

10. [10]

    WEI J,YANG H,WANG R.Optimal reinsurance and dividend strategies under the Markov-modulated insurance risk model[J].Stochastic Analysis and Applications,2010,28(6):1078.

11. [11]

    LI S,LU Y.Moments of the dividend payments and related problems in a Markov-modulated risk model[J].North American Actuarial Journal,2007,11(2):65.

12. [12]

    ANDRONOV A,GERTSBAKH I B.Signatures in Markov-modulated processes[J].Stochastic Models,2014,30(1):1.

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