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The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the…

Portfolio Management · Quantitative Finance 2014-10-16 Lingjiong Zhu

We study a discrete-time multi-period portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the excess of Conditional Value-at-Risk over expected terminal wealth. The…

Portfolio Management · Quantitative Finance 2026-04-17 Jérôme Lelong , Véronique Maume-Deschamps , William Thevenot

Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…

Methodology · Statistics 2024-09-12 Ruike Wu , Yanrong Yang , Han Lin Shang , Huanjun Zhu

Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…

Systems and Control · Electrical Eng. & Systems 2025-08-12 Alexandros E. Tzikas , Lukas Fiechtner , Arec Jamgochian , Mykel J. Kochenderfer

We study investment and insurance demand decisions for an agent in a theoretical continuous-time expected utility maximization model that combines risky assets with an (exogenous) insurable background risk. This risk takes the form of a…

Mathematical Finance · Quantitative Finance 2023-03-09 Hugo E. Ramirez , Rafael Serrano

We introduce a novel approach to solving the optimal portfolio choice problem under Epstein-Zin utility with a time-varying consumption constraint, where analytical expressions for the value function and the dual value function are not…

Optimization and Control · Mathematics 2025-02-24 Dejian Tian , Weidong Tian , Zimu Zhu

We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market…

Portfolio Management · Quantitative Finance 2017-01-12 Gonçalo Simões , Mark McDonald , Stacy Williams , Daniel Fenn , Raphael Hauser

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded…

Portfolio Management · Quantitative Finance 2012-11-07 Salvatore Federico , Paul Gassiat

This paper presents a deep reinforcement learning (DRL) framework for dynamic portfolio optimization under market uncertainty and risk. The proposed model integrates a Sharpe ratio-based reward function with direct risk control mechanisms,…

Portfolio Management · Quantitative Finance 2025-11-17 Emmanuel Lwele , Sabuni Emmanuel , Sitali Gabriel Sitali

This note lays part of the theoretical ground for a definition of differential systems modeling reinforcement learning in continuous time non-Markovian rough environments. Specifically we focus on optimal relaxed control of rough equations…

Optimization and Control · Mathematics 2024-02-29 Prakash Chakraborty , Harsha Honnappa , Samy Tindel

In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the…

Pricing of Securities · Quantitative Finance 2022-01-07 Zuo Quan Xu , Fahuai Yi

In this study, we propose a new multi-objective portfolio optimization with idiosyncratic and systemic risks for financial networks. The two risks are measured by the idiosyncratic variance and the network clustering coefficient derived…

Portfolio Management · Quantitative Finance 2021-11-23 Yajie Yang , Longfeng Zhao , Lin Chen , Chao Wang , Jihui Han

In a reinforcement learning (RL) setting, the agent's optimal strategy heavily depends on her risk preferences and the underlying model dynamics of the training environment. These two aspects influence the agent's ability to make…

Machine Learning · Computer Science 2025-09-23 Anthony Coache , Sebastian Jaimungal

In this paper we continue investigating the optimal dividend and investment problems under the Sparre Andersen model. More precisely, we assume that the claim frequency is a renewal process instead of a standard compound Poisson process,…

Probability · Mathematics 2019-09-02 Lihua Bai , Jin Ma

We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…

Portfolio Management · Quantitative Finance 2021-11-04 Jörn Sass , Dorothee Westphal

We study non-rectangular robust Markov decision processes under the average-reward criterion, where the ambiguity set couples transition probabilities across states and the adversary commits to a stationary kernel for the entire horizon. We…

Optimization and Control · Mathematics 2026-03-11 Shengbo Wang , Nian Si

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. The viability of robo-advisors crucially depends on their ability to offer personalized financial advice. We introduce a…

Portfolio Management · Quantitative Finance 2020-11-25 Agostino Capponi , Sveinn Olafsson , Thaleia Zariphopoulou

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is…

Portfolio Management · Quantitative Finance 2018-10-30 Sona Kilianova , Daniel Sevcovic

The objectives of option hedging/trading extend beyond mere protection against downside risks, with a desire to seek gains also driving agent's strategies. In this study, we showcase the potential of robust risk-aware reinforcement learning…

Computational Finance · Quantitative Finance 2023-12-27 David Wu , Sebastian Jaimungal

We use an optimization procedure based on simulated bifurcation (SB) to solve the integer portfolio and trading trajectory problem with an unprecedented computational speed. The underlying algorithm is based on a classical description of…

Computational Finance · Quantitative Finance 2020-09-18 Kyle Steinhauer , Takahisa Fukadai , Sho Yoshida