# American Institute of Mathematical Sciences

January  2018, 3: 5 doi: 10.1186/s41546-018-0031-1

## Zero covariation returns

 1. Robert H. Smith School of Business, University of Maryland, College Park 20742, MD, USA; 2. Department of Mathematics, K. U. Leuven, Leuven, Belgium

Received  November 26, 2017 Revised  May 07, 2018

Asset returns are modeled by locally bilateral gamma processes with zero covariations. Covariances are then observed to be consequences of randomness in variations. Support vector machine regressions on prices are employed to model the implied randomness. The contributions of support vector machine regressions are evaluated using reductions in the economic cost of exposure to prediction residuals. Both local and global mean reversion and momentum are represented by drift dependence on price levels. Optimal portfolios maximize conservative portfolio values calculated as distorted expectations of portfolio returns observed on simulated path spaces. They are also shown to outperform classical alternatives.
Citation: Dilip B. Madan, Wim Schoutens. Zero covariation returns. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 5-. doi: 10.1186/s41546-018-0031-1
##### References:

show all references

##### References:
 [1] Guangjun Shen, Xueying Wu, Xiuwei Yin. Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 755-774. doi: 10.3934/dcdsb.2020133 [2] Bing Liu, Ming Zhou. Robust portfolio selection for individuals: Minimizing the probability of lifetime ruin. Journal of Industrial & Management Optimization, 2021, 17 (2) : 937-952. doi: 10.3934/jimo.2020005 [3] Junkee Jeon. Finite horizon portfolio selection problems with stochastic borrowing constraints. Journal of Industrial & Management Optimization, 2021, 17 (2) : 733-763. doi: 10.3934/jimo.2019132 [4] Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial & Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130 [5] Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020451 [6] Kung-Ching Chang, Xuefeng Wang, Xie Wu. On the spectral theory of positive operators and PDE applications. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3171-3200. doi: 10.3934/dcds.2020054 [7] Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166 [8] Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133 [9] Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020458 [10] Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 [11] Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310 [12] Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051 [13] Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276 [14] Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127 [15] Van Duong Dinh. Random data theory for the cubic fourth-order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (2) : 651-680. doi: 10.3934/cpaa.2020284 [16] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065 [17] Beom-Seok Han, Kyeong-Hun Kim, Daehan Park. A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $C^{1}$ domains. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021002

Impact Factor: