Portfolio optimization for pension plans under hybrid stochastic and local volatility

Sung-Jin Yang; Jeong-Hoon Kim; Min-Ku Lee

Applications of Mathematics (2015)

  • Volume: 60, Issue: 2, page 197-215
  • ISSN: 0862-7940

Abstract

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Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result is a generalization of Merton's strategy in terms of the stochastic volatility and the elasticity of variance.

How to cite

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Yang, Sung-Jin, Kim, Jeong-Hoon, and Lee, Min-Ku. "Portfolio optimization for pension plans under hybrid stochastic and local volatility." Applications of Mathematics 60.2 (2015): 197-215. <http://eudml.org/doc/269889>.

@article{Yang2015,
abstract = {Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result is a generalization of Merton's strategy in terms of the stochastic volatility and the elasticity of variance.},
author = {Yang, Sung-Jin, Kim, Jeong-Hoon, Lee, Min-Ku},
journal = {Applications of Mathematics},
keywords = {pension plan; portfolio optimization; constant elasticity of variance; stochastic volatility; asymptotic analysis; pension plan; portfolio optimization; constant elasticity of variance; stochastic volatility; asymptotic analysis},
language = {eng},
number = {2},
pages = {197-215},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Portfolio optimization for pension plans under hybrid stochastic and local volatility},
url = {http://eudml.org/doc/269889},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Yang, Sung-Jin
AU - Kim, Jeong-Hoon
AU - Lee, Min-Ku
TI - Portfolio optimization for pension plans under hybrid stochastic and local volatility
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 197
EP - 215
AB - Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result is a generalization of Merton's strategy in terms of the stochastic volatility and the elasticity of variance.
LA - eng
KW - pension plan; portfolio optimization; constant elasticity of variance; stochastic volatility; asymptotic analysis; pension plan; portfolio optimization; constant elasticity of variance; stochastic volatility; asymptotic analysis
UR - http://eudml.org/doc/269889
ER -

References

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  1. Asch, M., Kohler, W., Papanicolaou, G., Postel, M., White, B., 10.1137/1033136, SIAM Rev. 33 519-625 (1991). (1991) Zbl0736.60055MR1137513DOI10.1137/1033136
  2. Beckers, S., 10.1111/j.1540-6261.1980.tb03490.x, Journal of Finance 35 661-673 (1980). (1980) DOI10.1111/j.1540-6261.1980.tb03490.x
  3. Boulier, J.-F., Huang, S., Taillard, G., 10.1016/S0167-6687(00)00073-1, Insur. Math. Econ. 28 173-189 (2001). (2001) Zbl0976.91034MR1835085DOI10.1016/S0167-6687(00)00073-1
  4. Boyle, P. P., Tian, Y. S., 10.2307/2676280, Journal of Financial and Quantitative Analysis 34 241-264 (1999). (1999) DOI10.2307/2676280
  5. Cerrai, S., 10.1214/08-AAP560, Ann. Appl. Probab. 19 899-948 (2009). (2009) Zbl1191.60076MR2537194DOI10.1214/08-AAP560
  6. Choi, S.-Y., Fouque, J.-P., Kim, J.-H., 10.1080/14697688.2013.780209, Quant. Finance 13 1157-1165 (2013). (2013) Zbl1281.91155MR3175894DOI10.1080/14697688.2013.780209
  7. Cox, J. C., 10.3905/jpm.1996.015, The Journal of Portfolio Management 23 15-17 (1996). (1996) DOI10.3905/jpm.1996.015
  8. Cox, J. C., Huang, C.-F., 10.1016/0022-0531(89)90067-7, J. Econ. Theory 49 33-83 (1989). (1989) Zbl0678.90011MR1024460DOI10.1016/0022-0531(89)90067-7
  9. Cox, J. C., Ross, S., 10.1016/0304-405X(76)90023-4, Journal of Financial Economics 3 145-166 (1976). (1976) DOI10.1016/0304-405X(76)90023-4
  10. Davydov, D., Linetsky, V., 10.1287/mnsc.47.7.949.9804, Manage. Sci. 47 949-965 (2001). (2001) DOI10.1287/mnsc.47.7.949.9804
  11. Deelstra, G., Grasselli, M., Koehl, P.-F., 10.1016/j.jedc.2003.10.003, J. Econ. Dyn. Control 28 2239-2260 (2004). (2004) Zbl1202.91124MR2078825DOI10.1016/j.jedc.2003.10.003
  12. Devolder, P., Princep, M. Bosch, Fabian, I. Dominguez, 10.1016/S0167-6687(03)00136-7, Insur. Math. Econ. 33 227-238 (2003). (2003) MR2039284DOI10.1016/S0167-6687(03)00136-7
  13. Fleming, W. H., Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Stochastic Modelling and Applied Probability 25 Springer, New York (2006). (2006) Zbl1105.60005MR2179357
  14. Fouque, J.-P, Papanicolaou, G., Sircar, K. R., Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press Cambridge (2000). (2000) Zbl0954.91025MR1768877
  15. Fouque, J.-P., Papanicolaou, G., Sircar, R., Sølna, K., Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, Cambridge University Press Cambridge (2011). (2011) Zbl1248.91003MR2867464
  16. Fredholm, I., 10.1007/BF02421317, Acta Math. 27 365-390 (1903), French. (1903) MR1554993DOI10.1007/BF02421317
  17. Gao, J., 10.1016/j.insmatheco.2009.01.005, Insur. Math. Econ. 44 479-490 (2009). (2009) Zbl1162.91411MR2519092DOI10.1016/j.insmatheco.2009.01.005
  18. Ghysels, E., Harvey, A., Renault, E., Stochastic volatility, Statistical Methods in Finance Handbook of Statistics 14 North-Holland, Amsterdam (1996). (1996) MR1602124
  19. Haberman, S., Vigna, E., 10.1016/S0167-6687(02)00128-2, Insur. Math. Econ. 31 35-69 (2002). (2002) Zbl1039.91025MR1956510DOI10.1016/S0167-6687(02)00128-2
  20. Harvey, C. R., 10.1016/S0927-5398(01)00036-6, Journal of Empirical Finance 8 573-637 (2001). (2001) DOI10.1016/S0927-5398(01)00036-6
  21. Jackwerth, J. C., Rubinstein, M., 10.1111/j.1540-6261.1996.tb05219.x, Journal of Finance 51 1611-1631 (1996). (1996) DOI10.1111/j.1540-6261.1996.tb05219.x
  22. Khas'minskii, R. Z., On stochastic processes defined by differential equations with a small parameter, Theory Probab. Appl. 11 211-228 (1966), translation from Teor. Veroyatn. Primen. 11 240-259 (1966), Russian. (1966) MR0203788
  23. Kim, J.-H., 10.1016/j.spa.2004.05.004, Stochastic Processes Appl. 114 161-174 (2004). (2004) Zbl1079.60055MR2094151DOI10.1016/j.spa.2004.05.004
  24. Merton, R. C., 10.1016/0022-0531(71)90038-X, J. Econ. Theory 3 373-413 (1971). (1971) Zbl1011.91502MR0456373DOI10.1016/0022-0531(71)90038-X
  25. Noh, E.-J., Kim, J.-H., 10.1016/j.jmaa.2010.09.055, J. Math. Anal. Appl. 375 510-522 (2011). (2011) Zbl1202.91302MR2735541DOI10.1016/j.jmaa.2010.09.055
  26. Øksendal, B., Stochastic Differential Equations. An Introduction with Applications, Universitext Springer, Berlin (2003). (2003) Zbl1025.60026MR2001996
  27. Papanicolaou, G. C., Stroock, D. W., Varadhan, S. R. S., Martingale approach to some limit theorems, Proc. Conf. Durham, 1976 Duke Univ. Math. Ser., Vol. III, Duke Univ., Durham (1977). (1977) Zbl0387.60067MR0461684
  28. Rubinstein, M., Nonparametric tests of alternative option pricing models using CBOE reported trades, Journal of Finance 40 455-480 (1985). (1985) 
  29. Xiao, J., Hong, Z., Qin, C., 10.1016/j.insmatheco.2006.04.007, Insur. Math. Econ. 40 302-310 (2007). (2007) Zbl1141.91473MR2286948DOI10.1016/j.insmatheco.2006.04.007
  30. Yuen, K. C., Yang, H., Chu, K. L., 10.1017/S1357321700002233, British Actuarial Journal 7 275-292 (2001). (2001) DOI10.1017/S1357321700002233

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