Review Articles

Increasing convex order of capital allocation with dependent assets under threshold model

Jiandong Zhang ,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China

jdzhang@nwnu.edu.cn

Zhouxia Guo ,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China

Jiale Niu ,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China

Rongfang Yan

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China; Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou, People's Republic of China

Pages | Received 15 Dec. 2022, Accepted 29 Dec. 2023, Published online: 10 Jan. 2024,
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In this manuscript, we consider a risk-preference investor allocating some amount of capital to the dependent risky asset, where the responding asset will occur default if the stochastic return is less than some predetermined threshold. Then, we present sufficient conditions of the increasing convex order on capital allocation with dependent risky assets when the stochastic return is right tail weakly stochastic arrangement increasing. Finally, some numerical examples are given as illustrations.

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References

  • Amini-Seresht, E., Zhang, Y., & Li, X. (2019). On asset allocation for a threshold model with dependent returns. European Actuarial Journal, 9(2), 559–574. https://doi.org/10.1007/s13385-019-00210-4
  • Ariyafar, S., Tata, M., Rezapour, M., & Madadi, M. (2020). Comparison of aggregation, minimum and maximum of two risky portfolios with dependent claims. Journal of Multivariate Analysis, 178, 104620. https://doi.org/10.1016/j.jmva.2020.10462
  • Balakrishnan, N., & Zhao, P. (2013). Ordering properties of order statistics from heterogeneous populations: A review with an emphasis on some recent developments. Probability in the Engineering and Informational Sciences, 27(4), 403–443. https://doi.org/10.1017/S026996481300015
  • Barmalzan, G., Najafabadi, A. T. P., & Balakrishnan, N. (2015). Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications. Insurance: Mathematics and Economics, 61, 235–241.
  • Boonen, T. J., Cheung, K. C., & Zhang, Y. (2021). Bowley reinsurance with asymmetric information on the insurer's risk preferences. Scandinavian Actuarial Journal, 2021(7), 623–644. https://doi.org/10.1080/03461238.2020.1867631
  • Cai, J., & Wei, W. (2014). Some new notions of dependence with applications in optimal allocation problems. Insurance: Mathematics and Economics, 55, 200–209.
  • Cai, J., & Wei, W. (2015). Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks. Journal of Multivariate Analysis, 138, 156–169. https://doi.org/10.1016/j.jmva.2014.12.011
  • Chen, R. (2003). Information economics. Nankai University Press.
  • Chen, Z., & Hu, T. (2008). Asset proportions in optimal portfolios with dependent default risks. Insurance: Mathematics and Economics, 43(2), 223–226.
  • Cheung, K. C., & Yang, H. (2004). Ordering optimal proportions in the asset allocation problem with dependent default risks. Insurance: Mathematics and Economics, 35(3), 595–609.
  • Denuit, M., Dhaene, J., Goovaerts, M., & Kaas, R. (2006). Actuarial theory for dependent risks: Measures, orders and models. John Wiley & Sons.
  • Ding, W., Wang, C., & Zhang, Y. (2021). Ordering properties of generalized aggregation with applications. Applied Stochastic Models in Business and Industry, 37(2), 282–302. https://doi.org/10.1002/asmb.v37.2
  • Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1–25. https://doi.org/10.1016/j.jfineco.2013.10.005
  • Giovagnoli, A., & Wynn, H. P. (2011). (u, v)-ordering and a duality theorem for risk aversion and Lorenz-type orderings. Preprint, arXiv:1108.1019.
  • Hadar, J., & Seo, T. K. (1988). Asset proportions in optimal portfolios. The Review of Economic Studies, 55(3), 459–468. https://doi.org/10.2307/2297395
  • Hagen, O. (1979). Towards a positive theory of preferences under risk. Springer.
  • Hennessy, D. A., & Lapan, H. E. (2002). The use of Archimedean copulas to model portfolio allocations. Mathematical Finance, 12(2), 143–154. https://doi.org/10.1111/mafi.2002.12.issue-2
  • Kijima, M., & Ohnishi, M. (1996). Portfolio selection problems via the bivariate characterization of stochastic dominance relations. Mathematical Finance, 6(3), 237–277. https://doi.org/10.1111/mafi.1996.6.issue-3
  • Landsberger, M., & Meilijson, I. (1990). Demand for risky financial assets: A portfolio analysis. Journal of Economic Theory, 50(1), 204–213. https://doi.org/10.1016/0022-0531(90)90092-X
  • Li, H., & Li, X. (2013). Stochastic orders in reliability and risk. Springer.
  • Li, X., & Li, C. (2016). On allocations to portfolios of assets with statistically dependent potential risk returns. Insurance: Mathematics and Economics, 68, 178–186.
  • Li, X., & You, Y. (2014). A note on allocation of portfolio shares of random assets with Archimedean copula. Annals of Operations Research, 212(1), 155–167. https://doi.org/10.1007/s10479-012-1137-y
  • Li, X., & You, Y. (2015). Permutation monotone functions of random vectors with applications in financial and actuarial risk management. Advances in Applied Probability, 47(1), 270–291. https://doi.org/10.1239/aap/1427814591
  • Ma, C. (2000). Convex orders for linear combinations of random variables. Journal of Statistical Planning and Inference, 84(1-2), 11–25. https://doi.org/10.1016/S0378-3758(99)00143-3
  • Marshall, A. W., Olkin, I., & Arnold, B. C. (1979). Inequalities: Theory of majorization and its applications (Vol. 143). Springer.
  • Rinott, Y., Scarsini, M., & Yu, Y. (2012). A colonel blotto gladiator game. Mathematics of Operations Research, 37(4), 574–590. https://doi.org/10.1287/moor.1120.0550
  • Scholes, M. S. (2000). Crisis and risk management. American Economic Review, 90(2), 17–21. https://doi.org/10.1257/aer.90.2.17
  • Shaked, M., & Shanthikumar, G. (2007). Stochastic orders. Springer Science Business Media.
  • Shane, S., & Venkataraman, S. (2000). The promise of entrepreneurship as a field of research. Academy of Management Review, 25(1), 217–226.
  • Xu, M., & Hu, T. (2012). Stochastic comparisons of capital allocations with applications. Insurance: Mathematics and Economics, 50(3), 293–298.
  • Yan, R., Zhang, J., & Zhang, Y. (2021). Optimal allocation of relevations in coherent systems. Journal of Applied Probability, 58(4), 1152–1169. https://doi.org/10.1017/jpr.2021.23
  • You, Y., & Li, X. (2015). Functional characterizations of bivariate weak SAI with an application. Insurance: Mathematics and Economics, 64, 225–231.
  • Zhang, J., Yan, R., & Wang, J. (2022). Reliability optimization of parallel-series and series-parallel systems with statistically dependent components. Applied Mathematical Modelling, 102, 618–639. https://doi.org/10.1016/j.apm.2021.10.003
  • Zhang, J., Yan, R., & Zhang, Y. (2023a). Reliability analysis of fail-safe systems with heterogeneous and dependent components subject to random shocks. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 237(6), 1073–1087. https://doi.org/10.1177/1748006X221122033
  • Zhang, J., Yan, R., & Zhang, Y. (2023b). Stochastic comparisons of largest claim amount from heterogeneous and dependent insurance portfolios. Journal of Computational and Applied Mathematics, 431, 115265. https://doi.org/10.1016/j.cam.2023.115265
  • Zhang, J., & Zhang, Y. (2022). A copula-based approach on optimal allocation of hot standbys in series systems. Naval Research Logistics (NRL), 69(6), 902–913. https://doi.org/10.1002/nav.v69.6
  • Zhang, J., & Zhang, Y. (2023). Stochastic comparisons of relevation allocation policies in coherent systems. TEST, 32, 865–907.
  • Zhang, Y. (2022). Stochastic comparisons on total capacity of weighted k-out-of-n systems with heterogeneous components. Statistical Theory and Related Fields, 6(1), 72–80. https://doi.org/10.1080/24754269.2021.1894402
  • Zhang, Y., & Cheung, K. C. (2020). On the increasing convex order of generalized aggregation of dependent random variables. Insurance: Mathematics and Economics, 92, 61–69.
  • Zhang, Y., Ding, W., & Zhao, P. (2018). On total capacity of k-out-of-n systems with random weights. Naval Research Logistics, 65(4), 347–359. https://doi.org/10.1002/nav.v65.4
  • Zhang, Y., & Zhao, P. (2015). Comparisons on aggregate risks from two sets of heterogeneous portfolios. Insurance: Mathematics and Economics, 65, 124–135.

To cite this article: Jiandong Zhang, Zhouxia Guo, Jiale Niu & Rongfang Yan (2024) Increasing convex order of capital allocation with dependent assets under threshold model, Statistical Theory and Related Fields, 8:2, 124-135, DOI: 10.1080/24754269.2023.2301630

To link to this article: https://doi.org/10.1080/24754269.2023.2301630