Derleme
BibTex RIS Kaynak Göster

İflas olasılığı kısıtı altında optimal reasürans üzerine bir derleme

Yıl 2016, Cilt: 9 Sayı: 1, 26 - 36, 25.06.2016

Öz

kullanılan yöntemler araştırılmıştır. Bu kapsamda, iflas olasılığına bağlı optimal reasüransın incelendiği
literatürdeki çalışmalar derlenerek kullanılan yöntemler sınıflandırılmıştır. Literatürdeki çalışmaların
incelenmesiyle iflas olasılığı kısıtı altında optimal reasürans üzerine yapılan çalışmaların düzeltme katsayısı
(adjustment coefficient), reasürans anlaşmaları, yatırım-optimizasyon teknikleri ve temettü ödemeleri olmak
üzere dört temel yaklaşım altında incelendiği belirlenmiştir.

Kaynakça

  • P. Azcue and N. Muler, 2005, Optimal reinsurance and dividend distribution policies in the Cramer-Lundberg model, Mathematical Finance, 15(2):261–308.
  • N. Bauerle, 2004, Approximation of optimal reinsurance and dividend payout policies, Mathematical Finance, 14:99–113.
  • C. J. Beveridge, D.C.M. Dickson, and X. Wu, 2008, Optimal dividends under reinsurance. Bulletin de lAssociation Suisse des Actuaires, 1(2):149–166.
  • N. L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones, and C. J. Nesbitt,1987, Actuarial Mathematics. Society of Actuaries.
  • H. Buhlmann, 1970, Mathematical Methods in Risk Theory. Grundlehren der mathematischen Wissenschaft: A series of comprehensive studies in mathematics. Springer,
  • B. Bulut Karageyik, 2015, Optimal Reinsurance under Competing Benefit Criteria, Ph.D Thesis, Department of Actuarial Sciences, Hacettepe University, Turkey.
  • M. T. Castillo, and G. Parrocha, 2003, Stochastic control theory for optimal investment. Working Paper, Department of Actuarial Studies, University of New South Wales, Australia.
  • M. L. Centeno, 1985, On combining quota-share and excess of loss. ASTIN Bulletin, 15(1):49–63.
  • M. L. Centeno, 1986, Measuring the effects of reinsurance by the adjustment coefficient. Insurance: Mathematics and Economics, 5(2):169 – 182.
  • M. L. Centeno, 1997, Excess of loss reinsurance and the probability of ruin in finite horizon, ASTIN Bulletin, 27(1), 59-70.
  • M. L. Centeno, 2002, Measuring the effects of reinsurance by the adjustment coefficient in the sparre anderson model. Insurance: Mathematics and Economics, 30(1):37 – 49.
  • M. L. Centeno and O. Simoes, 2009, Optimal reinsurance. Revista de la Real Academia de Ciencias Exactas Fsicas y Naturales Serie A-Matematicas, 103(2):387–405.
  • B. De Finetti, 1940, Il Problema Dei Pieni. Istituto italiano degli attuari.
  • B. De Finetti, 1957, Su un'impostazione alternativa della teoria collettiva del rischio, Transactions of the XVth International Congress of Actuaries, vol.2, 433-443.
  • D. C. M. Dickson and H. R. Waters, 1996, Reinsurance and ruin. Insurance: Mathematics and Economics, 19:61–80.
  • D. C. M. Dickson and H. R. Waters, 1997, Relative reinsurance retention levels. ASTIN Bulletin, 27:207–227.
  • D. C. M. Dickson and H. R. Waters, 2004, Some optimal dividends problems. ASTIN Bulletin, 34(1):49– 74.
  • D. C. M. Dickson and H. R. Waters, 2006, Optimal dynamic reinsurance. ASTIN Bulletin, 36(2):415–432.
  • J. Gaier and P. Grandits, 2002, Ruin probabilities in the presence of regularly varying tails and optimal Investment. Insurance: Mathematics and Economics, 30(2):211–217.
  • H. U. Gerber, 1969, Entscheidungskriterien f¨ur den zusammengesetzten Poisson-Prozess. Diss. Math. ETH Zrich, Nr. 4383, 0000. Ref.: Buhlmann, H. ; Korref.: Huber, P.
  • H. U. Gerber, 1979, An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph 8, Wharton School, University of Pennsylvania.
  • M. Guerra and M. L. Centeno, 2008, Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria. Insurance: Mathematics and Economics, 42(2):529– 539.
  • O. Hesselager, 1990, Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal, 1-2(1990):80–95.
  • C. Hipp and M. Plum, 2000, Optimal investment for insurers. Insurance: Mathematics and Economics, 27(2):215 – 228.
  • C. Hipp and M. Vogt, 2003, Optimal dynamic XL reinsurance. ASTIN Bulletin, 33(2):193–207.
  • C. Hipp, 2004, Stochastic Control with Application in Insurance. In Stochastic Methods in Finance, volume 1856 of Lecture Notes in Mathematics, pages 127–164. Springer Berlin Heidelberg.
  • Z. G. Ignatov, V. K. Kaishev and R. S. Krachunov, 2004, Optimal retention levels, given the joint survival of cedent and reinsurer. Scandinavian Actuarial Journal, 2004(6):401–430.
  • C. Irgens and J. Paulsen, 2004, Optimal control of risk exposure, reinsurance and investments for insurance portfolios. Insurance: Mathematics and Economics, 35(1):21 –51.
  • A. Joseph, 2013, Minimizing the Probability of Ultimate Ruin by Excess of Loss Reinsurance and Investments. Master’s thesis, University of Dar es salaam.
  • R. Kaas, M. Goovaerts, J. Dhaene and M. Denuit, 2008, Modern Actuarial Risk Theory-Using R. Springer- Verlag Berlin Heidelberg.
  • V. K. Kaishev and S.D. Dimitrina, 2006, Excess of loss reinsurance under joint survival optimality. Insurance: Mathematics and Economics, 39(3):376 – 389.
  • C. Kasumo, 2011, Minimizing Probability of Ultimate Ruin by Proportional Reinsurance and Investment. Master’s thesis, University of Dar es salaam.
  • M. Kaluszka, 2005, Truncated stop loss as optimal reinsurance agreement in one-period models. ASTIN Bulletin, 35(2):337–349.
  • E. T. Kolkovska, 2008, Minimizing the ruin probability of risk processes with reinsurance. International Journal of Pure and Applied Mathematics, 1(46):83–93.
  • Z. Liang and J. Guo, 2007, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23(2):333–350.
  • Z. Liang and J. Yao, 2010, Optimization of Dividend and Reinsurance Strategies Under Ruin Probability Constraint. ArXiv e-prints. Quantitative Finance Papers,1-31.
  • C. S. Liu and H. Yang, 2004, Optimal investment for a insurer to minimize its probability of ruin. North American Actuarial Journal, 8(2):11–31.
  • J. Ma, L. Bai and J. Liu, 2008, Minimizing the probability of ruin under interest force. Applied Mathematical Sciences, 17:843–851.
  • H. Meng. and T.K. Siu, 2011, On optimal reinsurance, dividend and reinvestment strategies. Economic Modelling, 28(12):211 – 218.
  • C. Nie, D.C.M. Dickson and S. Li, 2011, Minimizing the ruin probability through capital injections. Annals of Actuarial Science, 5(2):195–209.
  • H. Schmidli, 2001, Optimal proportional reinsurance policies in a dynamic setting. Scandinavian Actuarial Journal, 2001(1):55–68.
  • H. Schmidli, 2002, On minimizing the ruin probability by investment and reinsurance. Annals of Applied Probability, 12:890–907.
  • H. Schmidli, 2004, Asymptotics of ruin probabilities for risk processes under optimal reinsurance and investment policies: The large claim case. Queueing Systems, 46(1-2):149–157.
  • H. Schmidli, 2006, Optimization in non-life insurance. Stochastic Models, 22:689–722.
  • M. Taksar and C. Markussen, 2003, Optimal dynamic reinsurance policies for large insurance portfolios. Finance and Stochastics, 7(1):97–121.
  • S. Thonhauser and H. Albrecher, 2007, Dividend maximization under consideration of the time value of ruin. Insurance: Mathematics and Economics, 41(1):163 – 184, 2007.
  • H. R. Waters, 1979, Excess of loss reinsurance limits. Scandinavian Actuarial Journal, (1):37–43.
  • H. R. Waters, 1983, Some mathematical aspects of reinsurance. Insurance: Mathematics and Economics, 2(1):17 – 26.
  • Y. Wu, 2013, Optimal reinsurance and dividend strategies with capital injections in Cramer-Lundberg approximation model. Bulletin of the Malaysian Mathematical Sciences Society, 36(1):193–210.
  • M. Zhou and K.C. Yuen, 2012, Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle. Economic Modelling, 29(2):198– 207.

A Review on Optimal Reinsurance under Ruin Probability Constraint

Yıl 2016, Cilt: 9 Sayı: 1, 26 - 36, 25.06.2016

Öz

reinsurance under the ruin probability constraint. In this context, we review the literature relevant to the

optimal reinsurance under the ruin probability constraint and categorized current methods. The literature

review on optimal reinsurance under the ruin probability constraint is mainly focus on four major aspects:

reinsurance arrangement, adjustment coefficient, investment and dynamic optimization techniques, and

dividend payments.

Kaynakça

  • P. Azcue and N. Muler, 2005, Optimal reinsurance and dividend distribution policies in the Cramer-Lundberg model, Mathematical Finance, 15(2):261–308.
  • N. Bauerle, 2004, Approximation of optimal reinsurance and dividend payout policies, Mathematical Finance, 14:99–113.
  • C. J. Beveridge, D.C.M. Dickson, and X. Wu, 2008, Optimal dividends under reinsurance. Bulletin de lAssociation Suisse des Actuaires, 1(2):149–166.
  • N. L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones, and C. J. Nesbitt,1987, Actuarial Mathematics. Society of Actuaries.
  • H. Buhlmann, 1970, Mathematical Methods in Risk Theory. Grundlehren der mathematischen Wissenschaft: A series of comprehensive studies in mathematics. Springer,
  • B. Bulut Karageyik, 2015, Optimal Reinsurance under Competing Benefit Criteria, Ph.D Thesis, Department of Actuarial Sciences, Hacettepe University, Turkey.
  • M. T. Castillo, and G. Parrocha, 2003, Stochastic control theory for optimal investment. Working Paper, Department of Actuarial Studies, University of New South Wales, Australia.
  • M. L. Centeno, 1985, On combining quota-share and excess of loss. ASTIN Bulletin, 15(1):49–63.
  • M. L. Centeno, 1986, Measuring the effects of reinsurance by the adjustment coefficient. Insurance: Mathematics and Economics, 5(2):169 – 182.
  • M. L. Centeno, 1997, Excess of loss reinsurance and the probability of ruin in finite horizon, ASTIN Bulletin, 27(1), 59-70.
  • M. L. Centeno, 2002, Measuring the effects of reinsurance by the adjustment coefficient in the sparre anderson model. Insurance: Mathematics and Economics, 30(1):37 – 49.
  • M. L. Centeno and O. Simoes, 2009, Optimal reinsurance. Revista de la Real Academia de Ciencias Exactas Fsicas y Naturales Serie A-Matematicas, 103(2):387–405.
  • B. De Finetti, 1940, Il Problema Dei Pieni. Istituto italiano degli attuari.
  • B. De Finetti, 1957, Su un'impostazione alternativa della teoria collettiva del rischio, Transactions of the XVth International Congress of Actuaries, vol.2, 433-443.
  • D. C. M. Dickson and H. R. Waters, 1996, Reinsurance and ruin. Insurance: Mathematics and Economics, 19:61–80.
  • D. C. M. Dickson and H. R. Waters, 1997, Relative reinsurance retention levels. ASTIN Bulletin, 27:207–227.
  • D. C. M. Dickson and H. R. Waters, 2004, Some optimal dividends problems. ASTIN Bulletin, 34(1):49– 74.
  • D. C. M. Dickson and H. R. Waters, 2006, Optimal dynamic reinsurance. ASTIN Bulletin, 36(2):415–432.
  • J. Gaier and P. Grandits, 2002, Ruin probabilities in the presence of regularly varying tails and optimal Investment. Insurance: Mathematics and Economics, 30(2):211–217.
  • H. U. Gerber, 1969, Entscheidungskriterien f¨ur den zusammengesetzten Poisson-Prozess. Diss. Math. ETH Zrich, Nr. 4383, 0000. Ref.: Buhlmann, H. ; Korref.: Huber, P.
  • H. U. Gerber, 1979, An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph 8, Wharton School, University of Pennsylvania.
  • M. Guerra and M. L. Centeno, 2008, Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria. Insurance: Mathematics and Economics, 42(2):529– 539.
  • O. Hesselager, 1990, Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal, 1-2(1990):80–95.
  • C. Hipp and M. Plum, 2000, Optimal investment for insurers. Insurance: Mathematics and Economics, 27(2):215 – 228.
  • C. Hipp and M. Vogt, 2003, Optimal dynamic XL reinsurance. ASTIN Bulletin, 33(2):193–207.
  • C. Hipp, 2004, Stochastic Control with Application in Insurance. In Stochastic Methods in Finance, volume 1856 of Lecture Notes in Mathematics, pages 127–164. Springer Berlin Heidelberg.
  • Z. G. Ignatov, V. K. Kaishev and R. S. Krachunov, 2004, Optimal retention levels, given the joint survival of cedent and reinsurer. Scandinavian Actuarial Journal, 2004(6):401–430.
  • C. Irgens and J. Paulsen, 2004, Optimal control of risk exposure, reinsurance and investments for insurance portfolios. Insurance: Mathematics and Economics, 35(1):21 –51.
  • A. Joseph, 2013, Minimizing the Probability of Ultimate Ruin by Excess of Loss Reinsurance and Investments. Master’s thesis, University of Dar es salaam.
  • R. Kaas, M. Goovaerts, J. Dhaene and M. Denuit, 2008, Modern Actuarial Risk Theory-Using R. Springer- Verlag Berlin Heidelberg.
  • V. K. Kaishev and S.D. Dimitrina, 2006, Excess of loss reinsurance under joint survival optimality. Insurance: Mathematics and Economics, 39(3):376 – 389.
  • C. Kasumo, 2011, Minimizing Probability of Ultimate Ruin by Proportional Reinsurance and Investment. Master’s thesis, University of Dar es salaam.
  • M. Kaluszka, 2005, Truncated stop loss as optimal reinsurance agreement in one-period models. ASTIN Bulletin, 35(2):337–349.
  • E. T. Kolkovska, 2008, Minimizing the ruin probability of risk processes with reinsurance. International Journal of Pure and Applied Mathematics, 1(46):83–93.
  • Z. Liang and J. Guo, 2007, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23(2):333–350.
  • Z. Liang and J. Yao, 2010, Optimization of Dividend and Reinsurance Strategies Under Ruin Probability Constraint. ArXiv e-prints. Quantitative Finance Papers,1-31.
  • C. S. Liu and H. Yang, 2004, Optimal investment for a insurer to minimize its probability of ruin. North American Actuarial Journal, 8(2):11–31.
  • J. Ma, L. Bai and J. Liu, 2008, Minimizing the probability of ruin under interest force. Applied Mathematical Sciences, 17:843–851.
  • H. Meng. and T.K. Siu, 2011, On optimal reinsurance, dividend and reinvestment strategies. Economic Modelling, 28(12):211 – 218.
  • C. Nie, D.C.M. Dickson and S. Li, 2011, Minimizing the ruin probability through capital injections. Annals of Actuarial Science, 5(2):195–209.
  • H. Schmidli, 2001, Optimal proportional reinsurance policies in a dynamic setting. Scandinavian Actuarial Journal, 2001(1):55–68.
  • H. Schmidli, 2002, On minimizing the ruin probability by investment and reinsurance. Annals of Applied Probability, 12:890–907.
  • H. Schmidli, 2004, Asymptotics of ruin probabilities for risk processes under optimal reinsurance and investment policies: The large claim case. Queueing Systems, 46(1-2):149–157.
  • H. Schmidli, 2006, Optimization in non-life insurance. Stochastic Models, 22:689–722.
  • M. Taksar and C. Markussen, 2003, Optimal dynamic reinsurance policies for large insurance portfolios. Finance and Stochastics, 7(1):97–121.
  • S. Thonhauser and H. Albrecher, 2007, Dividend maximization under consideration of the time value of ruin. Insurance: Mathematics and Economics, 41(1):163 – 184, 2007.
  • H. R. Waters, 1979, Excess of loss reinsurance limits. Scandinavian Actuarial Journal, (1):37–43.
  • H. R. Waters, 1983, Some mathematical aspects of reinsurance. Insurance: Mathematics and Economics, 2(1):17 – 26.
  • Y. Wu, 2013, Optimal reinsurance and dividend strategies with capital injections in Cramer-Lundberg approximation model. Bulletin of the Malaysian Mathematical Sciences Society, 36(1):193–210.
  • M. Zhou and K.C. Yuen, 2012, Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle. Economic Modelling, 29(2):198– 207.
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Başak Bulut Karageyik

Şule Şahin Bu kişi benim

Yayımlanma Tarihi 25 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 9 Sayı: 1

Kaynak Göster

IEEE B. B. Karageyik ve Ş. Şahin, “A Review on Optimal Reinsurance under Ruin Probability Constraint”, JSSA, c. 9, sy. 1, ss. 26–36, 2016.