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Optimal insurance in a changing economy
1. | School of Insurance, Central University Of Finance and Economics, Beijing 100081 |
2. | Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
3. | Cass Business School, City University London, London, EC1Y 8TZ, United Kingdom |
4. | Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong, China |
References:
[1] |
N. U. Ahmed and K. L. Teo, Optimal Control of Distributed Parameter Systems, North Holland, New York-Amsterdam, 1981. |
[2] |
K. J. Arrow, Uncertainty and the welfare economics of medical care, American Economic Review, 53 (1963), 941-973, available at http://www.aeaweb.org/aer/top20/53.5.941-973.pdf. |
[3] |
C. Blanchet-Scalliet, N. E. Karoui, M. Jeanblanc and L. Martellini, Optimal investment and consumption decisions when time-horizon is uncertain, Journal of Mathematical Economics, 44 (2008), 1100-1113.
doi: 10.1016/j.jmateco.2007.09.004. |
[4] |
B. Bouchard and H. Pham, Wealth-path dependent utility maximization in incomplete markets, Finance Stochast, 8 (2004), 579-603.
doi: 10.1007/s00780-004-0125-8. |
[5] |
E. Briys, Insurance and consumption: The continuous-time case, Journal of Risk and Insurance, 53 (1986), 718-723.
doi: 10.2307/252972. |
[6] |
J. Buffington and R. J. Elliott, Regime switching and European options, Stochastic Theory and Control, LNCIS 280, (ed. B. Pasik-Duncan), LNCIS 280, 73-82, Springer-Verlag, Berlin, Heidelberg, 2002.
doi: 10.1007/3-540-48022-6_5. |
[7] |
J. Buffington and R. J. Elliott, American options with regime switching, International Journal of Theoretical and Applied Finance, 5 (2002), 497-514.
doi: 10.1142/S0219024902001523. |
[8] |
L. Delong, Optimal investment and consumption in the presence of default on a financial market driven by a Levy noise, Ann. Univ. Mariae Curie-Sk?odowska Sect. A, 60 (2006), 1-15. |
[9] |
R. J. Elliott, L. Aggoun and J. B. Moore, Hidden Markov Models: Imation and Control, Applications of Mathematics (New York), 29. Springer-Verlag, New York, 1995. |
[10] |
R. J. Elliott, L. L. Chan and T. K. Siu, Option pricing and Esscher transform under regime switching, Annals of Finance, 1 (2005), 423-432.
doi: 10.1007/s10436-005-0013-z. |
[11] |
R. J. Elliott and J. Hinz, Portfolio analysis, hidden Markov models and chart analysis by PF-Diagrams, International Journal of Theoretical and Applied Finance, 5 (2002), 385-399. |
[12] |
R. J. Elliott, T. K. Siu and L. L. Chan, Pricing volatility swaps under Heston's stochastic volatility model with regime switching, Applied Mathematical Finance, 14 (2007), 41-62.
doi: 10.1080/13504860600659222. |
[13] |
H. U. Gerber and E. W. Shiu, Investing for retirement: Optimal capital growth and dynamic asset allocation (with discussions), North American Actuarial Journal, 4 (2000), 42-62.
doi: 10.1080/10920277.2000.10595899. |
[14] |
S. M. Goldfeld and R. E. Quandt, The estimation of structural shifts by switching regressions, Annals of Economic and Social Measurement, 2 (1973), 475-485. |
[15] |
C. Gollier, Insurance and precautionary capital accumulation in a continuous-time model, Journal of Risk and Insurance, 61 (1994) 78-95.
doi: 10.2307/253425. |
[16] |
X. Guo, Information and option pricings, Quantitative Finance, 1 (2001), 38-44.
doi: 10.1080/713665550. |
[17] |
J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.
doi: 10.2307/1912559. |
[18] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51 (1969), 247-257.
doi: 10.2307/1926560. |
[19] |
R. C. Merton, Optimal consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[20] |
J. Mossin, Aspects of rational insurance purchasing, Journal of Political Economy, 76 (1968), 553-568.
doi: 10.1086/259427. |
[21] |
K. S. Moore and V. R. Young, Optimal insurance in a continuous-time model, Insurance Mathematics and Economics, 39 (2006), 47-68.
doi: 10.1016/j.insmatheco.2006.01.009. |
[22] |
R. E. Quandt, The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association, 53 (1958), 873-880.
doi: 10.1080/01621459.1958.10501484. |
[23] |
H. Schlesinger and C. Gollier, Second-best insurance contract design in an incomplete market, Scandinavian Journal of Economics, 97 (1995), 123-135. |
[24] |
K. L. Teo, D. W. Reid and I. E. Boyd, Stochastic optimal control theory and its computational method, International Journal on Systems Science, 11 (1980), 77-95.
doi: 10.1080/00207728008966998. |
[25] |
H. Tong, Some comments on the Canadian lynx data (with discussion), Journal of the Royal Statistical Society, Series A, General, 140 (1977), 432-436. |
[26] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 1979-989.
doi: 10.1016/j.automatica.2010.02.027. |
show all references
References:
[1] |
N. U. Ahmed and K. L. Teo, Optimal Control of Distributed Parameter Systems, North Holland, New York-Amsterdam, 1981. |
[2] |
K. J. Arrow, Uncertainty and the welfare economics of medical care, American Economic Review, 53 (1963), 941-973, available at http://www.aeaweb.org/aer/top20/53.5.941-973.pdf. |
[3] |
C. Blanchet-Scalliet, N. E. Karoui, M. Jeanblanc and L. Martellini, Optimal investment and consumption decisions when time-horizon is uncertain, Journal of Mathematical Economics, 44 (2008), 1100-1113.
doi: 10.1016/j.jmateco.2007.09.004. |
[4] |
B. Bouchard and H. Pham, Wealth-path dependent utility maximization in incomplete markets, Finance Stochast, 8 (2004), 579-603.
doi: 10.1007/s00780-004-0125-8. |
[5] |
E. Briys, Insurance and consumption: The continuous-time case, Journal of Risk and Insurance, 53 (1986), 718-723.
doi: 10.2307/252972. |
[6] |
J. Buffington and R. J. Elliott, Regime switching and European options, Stochastic Theory and Control, LNCIS 280, (ed. B. Pasik-Duncan), LNCIS 280, 73-82, Springer-Verlag, Berlin, Heidelberg, 2002.
doi: 10.1007/3-540-48022-6_5. |
[7] |
J. Buffington and R. J. Elliott, American options with regime switching, International Journal of Theoretical and Applied Finance, 5 (2002), 497-514.
doi: 10.1142/S0219024902001523. |
[8] |
L. Delong, Optimal investment and consumption in the presence of default on a financial market driven by a Levy noise, Ann. Univ. Mariae Curie-Sk?odowska Sect. A, 60 (2006), 1-15. |
[9] |
R. J. Elliott, L. Aggoun and J. B. Moore, Hidden Markov Models: Imation and Control, Applications of Mathematics (New York), 29. Springer-Verlag, New York, 1995. |
[10] |
R. J. Elliott, L. L. Chan and T. K. Siu, Option pricing and Esscher transform under regime switching, Annals of Finance, 1 (2005), 423-432.
doi: 10.1007/s10436-005-0013-z. |
[11] |
R. J. Elliott and J. Hinz, Portfolio analysis, hidden Markov models and chart analysis by PF-Diagrams, International Journal of Theoretical and Applied Finance, 5 (2002), 385-399. |
[12] |
R. J. Elliott, T. K. Siu and L. L. Chan, Pricing volatility swaps under Heston's stochastic volatility model with regime switching, Applied Mathematical Finance, 14 (2007), 41-62.
doi: 10.1080/13504860600659222. |
[13] |
H. U. Gerber and E. W. Shiu, Investing for retirement: Optimal capital growth and dynamic asset allocation (with discussions), North American Actuarial Journal, 4 (2000), 42-62.
doi: 10.1080/10920277.2000.10595899. |
[14] |
S. M. Goldfeld and R. E. Quandt, The estimation of structural shifts by switching regressions, Annals of Economic and Social Measurement, 2 (1973), 475-485. |
[15] |
C. Gollier, Insurance and precautionary capital accumulation in a continuous-time model, Journal of Risk and Insurance, 61 (1994) 78-95.
doi: 10.2307/253425. |
[16] |
X. Guo, Information and option pricings, Quantitative Finance, 1 (2001), 38-44.
doi: 10.1080/713665550. |
[17] |
J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.
doi: 10.2307/1912559. |
[18] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51 (1969), 247-257.
doi: 10.2307/1926560. |
[19] |
R. C. Merton, Optimal consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[20] |
J. Mossin, Aspects of rational insurance purchasing, Journal of Political Economy, 76 (1968), 553-568.
doi: 10.1086/259427. |
[21] |
K. S. Moore and V. R. Young, Optimal insurance in a continuous-time model, Insurance Mathematics and Economics, 39 (2006), 47-68.
doi: 10.1016/j.insmatheco.2006.01.009. |
[22] |
R. E. Quandt, The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association, 53 (1958), 873-880.
doi: 10.1080/01621459.1958.10501484. |
[23] |
H. Schlesinger and C. Gollier, Second-best insurance contract design in an incomplete market, Scandinavian Journal of Economics, 97 (1995), 123-135. |
[24] |
K. L. Teo, D. W. Reid and I. E. Boyd, Stochastic optimal control theory and its computational method, International Journal on Systems Science, 11 (1980), 77-95.
doi: 10.1080/00207728008966998. |
[25] |
H. Tong, Some comments on the Canadian lynx data (with discussion), Journal of the Royal Statistical Society, Series A, General, 140 (1977), 432-436. |
[26] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 1979-989.
doi: 10.1016/j.automatica.2010.02.027. |
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