Introduction of New Risk Metric using Kernel Density Estimation Via Linear Diffusion
Subject Areas : Risk ManagementAhmad Darestani Farahani 1 , Mohammadreza Miri Lavasani 2 , Hamidreza Kordlouie 3 , Ghodratallah Talebnia 4
1 - Department of Finance, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of HSE, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Financial Management, Eslamshahr Branch, Islamic Azad University, Tehran, Iran
4 - Department of Accounting, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Keywords:
Abstract :
References
[1] Markowitz, H.M., Portfolio selection, Journal of Finance, 1952, 7, P. 77–91. Doi: 10.2307/2975974.
[2] Lien, D., and Tse, Y K., Hedging downside risk with futures contracts, Applied Financial Economics, 2000, 10(2), P. 163–170. Doi: 10.1080/096031000331798.
[3] Miryekemami, S.A., Sadeh, E., and Amini Sabegh, Z., Using Genetic Algorithm in Solving Stochastic Programming for Multi-Objective Portfolio Selection in Tehran Stock Exchange, Advances in Mathematical Finance and Applications, 2017, 2(4), P. 107-120. Doi: 10.22034/AMFA.2017.536271.
[4] Navidi, S., Rostamy-Malkhalifeh, M., and Banihashemi, S., Using MODEA and MODM with Different Risk Measures for Portfolio Optimization, Advances in Mathematical Finance and Applications, 2020, 5(1), P. 29-51. Doi: 10.22034/AMFA.2019.1864620.1200.
[5] Rahmani, M., Khalili Eraqi, M., and Nikoomaram, H., Portfolio Optimization by Means of Meta Heuristic Algorithms, Advances in Mathematical Finance and Applications, 2019, 4(4), P.83-97.
Doi: 10.22034/AMFA.2019.579510.1144.
[6] Fix, E., and Hodges, J.L., Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties, International Statistical Review, 1989, 57(1), P.238-247. Doi: 10.2307/1403797.
[7] Silverman, B.W., Jones M.C., E. Fix and J.L. Hodges (1951) An Important Contribution to Nonparametric Discriminant analysis and Density Estimation, International Statistical Review, 1989, 57(3). P. 233-247. Doi: 10.2307/1403796.
[8] Gyorfi, L., Kohler, M., Krzyzak, A., and Walk, H., A Distribution-Free Theory of Nonparametric Regression, Springer Series in Statistics, 2002, P. 9-12. Doi: 10.1007/b97848.
[9] Roy, A.D., Safety first and the holding of assets, Econometrica, 1952, 20, P. 431- 449. Doi: 10.2307/1907413.
[10] Rom, B.M. and Ferguson, K., Post-Modern Portfolio Theory Comes of Age, Journal of Investing, 1993, 2(4), P. 27-33. Doi: 10.3905/joi.2.4.27.
[11] Adams, J. and Montesi, C. J., Major Issues Related to Hedge Accounting, Financial Accounting Standard Board, 1995, Newark, Connecticut. Bib ID: 1091732.
[12] Lien, D., Tse, Y.K., Hedging time-varying downside risk, Journal of Futures Markets, 1998, 18, P. 705–722. Doi: 10.1002/(SICI)1096-9934(199809)18.
[13] Lien, D., and Tse, Y. K., Hedging downside risk with futures contracts, Applied Financial Economics, 2000, 10(2), P. 163–170. Doi: 10.1080/096031000331798.
[14] Chen, S.S., Lee, C.F., and Shrestha, K., Empirical analysis of the relationship between the hedge ratio and hedging horizon: A simultaneous estimation of the short- and long-run hedge ratios, Journal of Futures Markets, 2004, 24, P. 359–386. Doi: 10.1002/fut.10121.
[15] Bond, S.A., and Satchell, S. E., Statistical properties of the sample semi-variance, Applied Mathematical Finance, 2002, 9(4), P. 219-239. Doi: 10.1080/1350486022000015850.
[16] Fishburn, P.C., Mean-risk analysis with risk associated with below target returns, American Economic Review, 1977, 67(2), P.116–126. Doi: 10.2307/1807225.
[17] Harlow, W.V., and Rao, R.K.S., Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence, Journal of Financial and Quantitative Analysis, 1989, 24, P. 285–311. Doi: 10.2307/2330813.
[18] Huang, X.X., Mean-semi variance models for fuzzy portfolio selection, Journal of Computational and Applied Mathematics, 2008, 217(1), P. 1-8. Doi: 10.1016/j.cam.2007.06.009.
[19] Porter, R.B., and Gaumnitz, J.E., Stochastic dominance vs. mean-variance portfolio analysis: An empirical evaluation, American Economic Review, 1972, 62(3), P. 438-446.
[20] Leibowitz, M.L. and Langetieg, T.C., Shortfall risk and the asset allocation decision: A simulation analysis of stock and bond risk profiles, Journal of Portfolio Management, 1989, P. 61-68. Doi: 10.3905/jpm.1989.409236
[21] Sortino, F. and Forsey, H., On the Use and Misuse of Downside Risk, The Journal of Portfolio Management, 1996, P. 381-408. Doi: 10.3905/jpm.1996.35.
[22] Rosenblatt, M., Remarks on some nonparametric estimates of a density function, Annals of Mathematical Statistics, 1956, 27, P. 832–837. Doi: 10.1214/aoms/1177728190.
[23] Silverman, B.W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, 1986, London. ISBN-13: 978-0412246203.
[24] Foster, D.P., and Nelson, D.B., Continuous Record Asymptotics for Rolling Sample Variance Estimators, Econometrica, 1996, 64(1), P. 139-174. Doi: 10.2307/2171927.
[25] Botev, Z.I., Grotowski, J.F., and Kroese, D.P., Kernel Density Estimation via Diffusion, The Annals of Statistics, 2010, 38(5), P.2916–2957. Doi: 10.1214/10-AOS799.
[26] Devroye, D., Beirlant, J., Fraiman, R., Hall, P., Jones, M. C., Logosi, G., Mammen, E., Marron, J.S., Sanchez-Sellero, C., de Una, J., Udina, F. and Devroye, L., Universal smoothing factor selection in density estimation: Theory and practice, Test, 1997, 6, P. 223–320. Doi: 10.1007/BF02564701.
[27] Jones, M.C., Marron, J.S., Sheather, S.J., A brief survey of bandwidth selection for density estimation, Journal of the American Statistical Association, 1996, 91, P. 401–407. Doi: 10.2307/2291420.
[28] Figueroa-Lópeza, J.E., and Li, C. Optimal kernel estimation of spot volatility of stochastic differential equations, Stochastic Processes and their Applications, 2020, 130(8), P. 4693-4720. Doi: 10.1016/j.spa.2020.01.013.
[29] Hogan, W.W. and Warren J.M., Computation of the Efficient Boundary in the E-S Portfolio Selection Model, Journal of Financial and Quantitative Analysis, 1972, 7(4), P. 1881-1896. Doi: 10.2307/2329623.
[30] Bawa. V.S., and Lienderberg E.B., Capital Market Equilibrium in a Mean-Lower Partial Moment Framework, Journal of Financial Economics, 1977, 5(2), P.189-200. Doi: 10.1016/0304-405X(77)90017-4.