Bi-objective reliability based optimization: an application to investment analysis

Portfolio optimization problems are easy to address if single linear objective functions are considered, with the assumption of normality of asset returns distributions, subject to different risks, returns, and investment constraints. Higher complexities arise if combinations of multi-objective formulations, non-linear assets, non-normal asset return distributions, and uncertainty in parameter estimates are studied. In this paper, we solve two interesting variants of multi-objective investment analysis problems considering both non-normal asset return distributions and uncertainty in parameter estimates. Data used for the optimization models are pre-processed using ARCH/GARCH combined with extreme value asset returns distribution (EVD). The efficacy of our proposed multi-objective reliability-based portfolio optimization (MORBPO) problems is validated using Indian financial market data (Details of plan of codes, pseudo-codes and other set of detailed runs results (not discussed in this paper) are given in the open access link, https://github.com/RNSengupta/Bi-Objective_RBDO_Paper). We present the optimal values of investment weights, portfolio returns, portfolio risks (variance, CVaR, EVaR), reliability indices (β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}) as well as Pareto optimal frontiers and analyze the outputs in the context of their practical implications. The run results highlight the fact that investors’ uncertainty levels (i.e., β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}) play a crucial role in deciding the investment outcomes and thus facilitates him/her in choosing the optimal risk-return combinations of the portfolios.