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Dynamic investment portfolio optimization using a multivariate Merton model with correlated jump risk | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 1331-1341 اصل مقاله (500.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23421.2538 | ||
| نویسندگان | ||
| Bahareh Afhami1؛ Mohsen Rezapour2؛ Mohsen Madadi* 1؛ Vahed Maroufy2 | ||
| 1Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Biostatistics \& Data Science, School of Public Health, The University of Texas Health Science Center at Houston (UTHealth), Houston, Texas | ||
| تاریخ دریافت: 24 اسفند 1399، تاریخ بازنگری: 27 اردیبهشت 1400، تاریخ پذیرش: 08 تیر 1400 | ||
| چکیده | ||
| In this paper, we are concerned with the optimization of a dynamic investment portfolio when the securities which follow a multivariate Merton model with dependent jumps are periodically invested and proceed by approximating the Condition-Value-at-Risk (CVaR) by comonotonic bounds and maximize the expected terminal wealth. Numerical studies, as well as applications of our results to real datasets, are also provided. | ||
| کلیدواژهها | ||
| Risk analysis؛ Conditional tail expectation؛ Merton Model؛ Geometric Brownian motion؛ Comonotonicity | ||
| مراجع | ||
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[1] B. Afhami, M. Rezapour, M. Madadi and V. Maroufy, Portfolio selection under multivariate merton model with correlated jump risk, (2021), arXiv preprint arXiv:2104.10240. [2] Z. Al-Zhour, M. Barfeie, F. Soleymani and E. Tohidi, A computational method to price with transaction costs under the nonlinear Black-Scholes model, Chaos, Solitons Fract. 127 (2019) 291–301. [3] T. Cura, Particle swarm optimization approach to portfolio optimization, Nonlinear Anal. Real World Appl. 10 (2009) 2396–2406. [4] J. Dhaene and R. Kaas, The concept of comonotonicity in actuarial science and finance: theory, Ins. Math. Econ. 31 (2002) 3–33. [5] J. Dhaene, S. Vanduffel, M. J. Goovaerts, R. Kaas, Q. Tang and D. Vyncke, Risk measures and comonotonicity: A review, Stoch. Mod. 22 (2006) 573–606. [6] Z. Jankova, Drawbacks and limitations of Black-Scholes model for options pricing, J. Fin. Stud. Res. 2018 (2018) Article ID 179814. [7] R. Kaas, J. Dhaene and M. J. Goovaerts, Upper and lower bounds for sums of random variables, Ins. Math. Econ. 27 (2000) 151–168. [8] W.H. Li, L. X. Liu, G. W. Lv and C.X. Li, Exchange option pricing in jump-diffusion models based on esscher transform, Commun. Statistics-Theory Meth. 47 (2018) 4661–4672. [9] L. Maclean, Y. Zhao and W. Ziemba, Dynamic portfolio selection with process control, J. Bank. Fin. 30 (2006) 317–339. [10] D. A. I. Maruddani, Abdurakhman and D. Safitri, The effect of extreme asset prices to the valuation of zero coupon bond with jump diffusion processes, J. Phys. Conf. Ser. 1217 (2019) 012075. [11] H. Markowitz, Portfolio selection, J. Fin. 7 (1952) 77–91. [12] R. Merton, Theory of rational option pricing, Bell J. Econ. Manag. Sci. 4 (1973) 141–183. [13] R. Merton, Option pricing when underlying stock returns are discontinuous, J. Fin. Econ. 3 (1976) 125–144. [14] J. St¨ubinger and S. Endres, Pairs trading with a mean-reverting jump-diffusion model on highfrequency data, FAU Discussion Papers in Economics, University of Erlangen-N¨urnberg, (2017). [15] L. Xu, Ch. Gao, G. Kou and Q. Liu, Comonotonic approximation to periodic investment problems under stochastic drift, Euro. J. Oper. Res. 262 (2017) 251–261. | ||
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