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A unified parameter identification method for nonlinear time-delay systems
Optimal portfolio in a continuous-time self-exciting threshold model
1. | China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China |
2. | Department of Actuarial Mathematics and Statistics, and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom |
3. | Cass Business School, City University, 106 Bunhill Row, London EC1Y 8TZ, United Kingdom |
4. | Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, China |
References:
[1] |
R. J. Elliott and P. E. Kopp, "Mathematics of Financial Markets,", $2^{nd}$ edition, (2005).
|
[2] |
S. M. Goldfeld and R. E. Quandt, A Markov model for switching regressions,, Journal of Econometrics, 1 (1973), 3. Google Scholar |
[3] |
J. D. Hamilton, A new approach to the economic analysis of non-stationary time series and the business cycle,, Econometrica, 57 (1989), 357.
doi: 10.2307/1912559. |
[4] |
B. G. Jang, H. K. Koo and M. Loewenstein, Liquidity premia and transaction costs,, Journal of Finance, 62 (2007), 2329. Google Scholar |
[5] |
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance,", Applications of Mathematics (New York), 39 (1998).
|
[6] |
J. Lintner, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets,, Review of Economics and Statistics, 47 (1965), 12. Google Scholar |
[7] |
H. M. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77. Google Scholar |
[8] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time model,, Review of Economics and Statistics, 51 (1969), 247. Google Scholar |
[9] |
R. C. Merton, Optimal consumption and portfolio rules in a continuous-time model,, Journal of Economic Theory, 3 (1971), 373.
|
[10] |
J. Mossin, Equilibrium in a capital asset market,, Econometrica, 34 (1966), 768. Google Scholar |
[11] |
R. E. Quandt, The estimation of parameters of linear regression system obeying two separate regimes,, Journal of the American Statistical Association, 53 (1958), 873.
|
[12] |
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming,, Review of Economics and Statistics, 51 (1969), 239. Google Scholar |
[13] |
W. F. Sharpe, Capital asset prices: A theory of market equilibrium under conditions of risk,, Journal of Finance, 19 (1964), 425. Google Scholar |
[14] |
H. Tong, On a threshold model,, in, (1978), 575. Google Scholar |
[15] |
H. Tong and K. S. Lim, Threshold autoregression, limit cycles and cyclical data (with discussion),, Journal of Royal Statistical Society - B, 42 (1980), 245. Google Scholar |
[16] |
H. Tong, "Threshold Models in Nonlinear Time Series Analysis,", Lecture Notes in Statistics, 21 (1983).
doi: 10.1007/978-1-4684-7888-4. |
[17] |
J. L. Treynor, Toward a theory of market value of risky assets,, unpublished manuscript., (). Google Scholar |
[18] |
G. Yin and X. Zhou, Markowitz's mean-variance portfolio selection with regime switching: From discrete-time models to their continuous-time limits,, IEEE Transactions on Automatic Control, 49 (2004), 349.
doi: 10.1109/TAC.2004.824479. |
[19] |
X. Zhou and G. Yin, Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model,, SIAM Journal on Control and Optimization, 42 (2003), 1466.
doi: 10.1137/S0363012902405583. |
show all references
References:
[1] |
R. J. Elliott and P. E. Kopp, "Mathematics of Financial Markets,", $2^{nd}$ edition, (2005).
|
[2] |
S. M. Goldfeld and R. E. Quandt, A Markov model for switching regressions,, Journal of Econometrics, 1 (1973), 3. Google Scholar |
[3] |
J. D. Hamilton, A new approach to the economic analysis of non-stationary time series and the business cycle,, Econometrica, 57 (1989), 357.
doi: 10.2307/1912559. |
[4] |
B. G. Jang, H. K. Koo and M. Loewenstein, Liquidity premia and transaction costs,, Journal of Finance, 62 (2007), 2329. Google Scholar |
[5] |
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance,", Applications of Mathematics (New York), 39 (1998).
|
[6] |
J. Lintner, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets,, Review of Economics and Statistics, 47 (1965), 12. Google Scholar |
[7] |
H. M. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77. Google Scholar |
[8] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time model,, Review of Economics and Statistics, 51 (1969), 247. Google Scholar |
[9] |
R. C. Merton, Optimal consumption and portfolio rules in a continuous-time model,, Journal of Economic Theory, 3 (1971), 373.
|
[10] |
J. Mossin, Equilibrium in a capital asset market,, Econometrica, 34 (1966), 768. Google Scholar |
[11] |
R. E. Quandt, The estimation of parameters of linear regression system obeying two separate regimes,, Journal of the American Statistical Association, 53 (1958), 873.
|
[12] |
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming,, Review of Economics and Statistics, 51 (1969), 239. Google Scholar |
[13] |
W. F. Sharpe, Capital asset prices: A theory of market equilibrium under conditions of risk,, Journal of Finance, 19 (1964), 425. Google Scholar |
[14] |
H. Tong, On a threshold model,, in, (1978), 575. Google Scholar |
[15] |
H. Tong and K. S. Lim, Threshold autoregression, limit cycles and cyclical data (with discussion),, Journal of Royal Statistical Society - B, 42 (1980), 245. Google Scholar |
[16] |
H. Tong, "Threshold Models in Nonlinear Time Series Analysis,", Lecture Notes in Statistics, 21 (1983).
doi: 10.1007/978-1-4684-7888-4. |
[17] |
J. L. Treynor, Toward a theory of market value of risky assets,, unpublished manuscript., (). Google Scholar |
[18] |
G. Yin and X. Zhou, Markowitz's mean-variance portfolio selection with regime switching: From discrete-time models to their continuous-time limits,, IEEE Transactions on Automatic Control, 49 (2004), 349.
doi: 10.1109/TAC.2004.824479. |
[19] |
X. Zhou and G. Yin, Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model,, SIAM Journal on Control and Optimization, 42 (2003), 1466.
doi: 10.1137/S0363012902405583. |
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