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This work introduces MORP-DRL, a deep reinforcement learning framework that jointly optimizes expected return and downside risk via variance, CVaR, and EVaR. Using GARCH(1,1), extreme value theory, and a t-copula with QMC scenario generation, it trains a PPO strategy with realistic transaction-cost and portfolio-bound constraints, outperforming NSGA-II across multiple market regimes.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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problem does the document address?","Question",{"text":63,"@type":64},"It addresses portfolio optimization under uncertainty as a bi-objective decision problem balancing expected return and downside risk under practical constraints and market dynamics.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does MORP-DRL model risk and uncertainty?",{"text":68,"@type":64},"It jointly optimizes expected return and downside risk using variance, CVaR, and EVaR, while modeling heavy-tailed behavior with GARCH(1,1), extreme value theory, and a t-copula dependence structure.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the proposed method trained and evaluated?",{"text":72,"@type":64},"A PPO-based strategy is developed with transaction costs and portfolio bounds, benchmarked against NSGA-II, and tested on ten global equity indices across pre-COVID, COVID, and post-COVID 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\nIndian Institute of Management Amritsar Amritsar, India [dassounaq@gmail.com](dassounaq@gmail.com)  \nTanmay Sen  \nSQC & OR Unit  \nIndian Statistical Institute Kolkata Kolkata, India [tanmay.sen@isical.ac.in](tanmay.sen@isical.ac.in)  \narXiv :2607 .066 10v 1 [ cs .LG] 7 Jul 2026  \nRaghu Nandan Sengupta  \nDepartment of Management Sciences Indian Institute of Technology Kanpur Kanpur – 208 016, India [raghus@iitk.ac.in](raghus@iitk.ac.in)  \nAditya Gupta  \nMcKinsey and Company Gurgaon, India  \n[aditya_gupta-guva@mckinsey.com](aditya_gupta-guva@mckinsey.com)  \nJuly 9, 2026  \nABSTRACT  \nPortfolio optimization under uncertainty is inherently a multi-objective decision problem involving complex interactions among return, risk, market dynamics, and practical investment constraints.  \nExisting reliability based portfolio optimization approaches primarily rely on static optimization frameworks and often fail to capture sequential decision making, tail risk, and market frictions such as transaction costs. To address these limitations, we propose a deep reinforcement learning framework for multi-objective reliability based portfolio optimization (MORP-DRL) . The proposed framework jointly optimizes expected return and downside risk using three complementary risk measures: variance, Conditional Value-at-Risk (CVaR), and Entropic Value-at-Risk (EVaR). To model uncertainty and heavy-tailed market behavior, asset returns are represented using GARCH(1,1), Extreme Value Theory, and a t-copula dependence structure, while realistic scenarios are generated through quasiMonte Carlo simulation. A Proximal Policy Optimization (PPO) based strategy is developed under practical constraints including transaction costs and portfolio bounds, and is benchmarked against NSGA-II. Experiments on ten global equity indices across pre-COVID, COVID, and post-COVID market regimes demonstrate that MORP-DRL achieves competitive risk-return performance, reduced downside risk during periods of market stress, and scalability to high-dimensional portfolio settings.  \nKeywords: Bi-objective, Portfolio Optimization, Deep Reinforcement Learning, Extreme Value Theory (EVT), Entropic Value-at-Risk (EVaR), NSGA-II , QMC, t-copula  \n1 Introduction  \nPortfolio optimization is one of the most fundamental problems in quantitative finance and investment management. The primary objective is to allocate capital among different financial assets in a way that balances expected return and investment risk while satisfying practical investment constraints. The seminal work of Markowitz [1, 2] introduced the modern portfolio theory (MPT), which formulated portfolio selection as a mean-variance optimization problem. This framework established the foundation of modern portfolio management by emphasizing diversification and the trade-off between return and risk. Subsequent developments, including the capital asset Pricing model (CAPM)  \n[3], Black-Litterman model, and factor based investment strategies, further extended classical portfolio theory by incorporating systematic market risk and investor preferences. Despite their importance, these traditional models rely on several simplifying assumptions, such as normally distributed returns, linear dependence structures, constant covariance  \nA PREPRINT-JULY 9, 2026  \nmatrices, and frictionless markets. However, financial markets behave very differently. Asset returns frequently exhibit sudden fluctuations, changing dependence patterns, periods of high volatility, and extreme market movements, particularly during financial crises and uncertain economic conditions. As a result, traditional variance-based approaches may not adequately capture downside and extreme market risks. To address these limitations, alternative downside risk measures have been extensively investigated in the literature. Value-at-Risk (VaR) [4] emerged as one of the earliest a","cbCaisRzLr9ArcUX","https://ap.wps.com/l/cbCaisRzLr9ArcUX","pdf",13201534,24,"English","# Abstract\n# 1 Introduction","[{\"question\":\"What problem does the document address?\",\"answer\":\"It addresses portfolio optimization under uncertainty as a bi-objective decision problem balancing expected return and downside risk under practical constraints and market dynamics.\"},{\"question\":\"How does MORP-DRL model risk and uncertainty?\",\"answer\":\"It jointly optimizes expected return and downside risk using variance, CVaR, and EVaR, while modeling heavy-tailed behavior with GARCH(1,1), extreme value theory, and a t-copula dependence structure.\"},{\"question\":\"How is the proposed method trained and evaluated?\",\"answer\":\"A PPO-based strategy is developed with transaction costs and portfolio bounds, benchmarked against NSGA-II, and tested on ten global equity indices across pre-COVID, COVID, and post-COVID regimes.\"}]","DEEP REINFORCEMENT LEARNING FOR RELIABILITY BASED BI-OBJECTIVE PORTFOLIO OPTIMIZATION | PDF",1789978745]