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This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…

Pricing of Securities · Quantitative Finance 2014-07-21 Leunglung Chan , Song-Ping Zhu

Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely…

Computational Finance · Quantitative Finance 2021-12-10 Kumar Yashaswi

This paper explores the mean-variance portfolio selection problem in a multi-period financial market characterized by regime-switching dynamics and uncontrollable liabilities. To address the uncertainty in the decision-making process within…

Optimization and Control · Mathematics 2025-09-04 Zhongqin Gao , Ping Chen , Xun Li , Yan Lv , Wenhao Zhang

In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor's attention to news is…

Optimization and Control · Mathematics 2022-05-19 Y. Zhang , Z. Jin , J. Wei , G. Yin

In this paper, we consider a variety of multi-state Hidden Markov models for predicting and explaining the Bitcoin, Ether and Ripple returns in the presence of state (regime) dynamics. In addition, we examine the effects of several…

Applications · Statistics 2020-12-08 Constandina Koki , Stefanos Leonardos , Georgios Piliouras

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…

Optimization and Control · Mathematics 2017-06-14 Peyman Mohajerin Esfahani , Daniel Kuhn

We study aleatoric and epistemic uncertainty estimation in a learned regressive system dynamics model. Disentangling aleatoric uncertainty (the inherent randomness of the system) from epistemic uncertainty (the lack of data) is crucial for…

Machine Learning · Computer Science 2025-03-21 Zhiyu An , Zhibo Hou , Wan Du

This article investigates a regime-switching investment strategy aimed at mitigating downside risk by reducing market exposure during anticipated unfavorable market regimes. We highlight the statistical jump model (JM) for market regime…

Portfolio Management · Quantitative Finance 2024-09-18 Yizhan Shu , Chenyu Yu , John M. Mulvey

The performance of machine learning (ML) models critically depends on the quality and representativeness of the training data. In applications with multiple heterogeneous data generating sources, standard ML methods often learn spurious…

In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less…

Applications · Statistics 2023-01-26 Patrick Aschermayr , Konstantinos Kalogeropoulos

With the improvement of computer performance and the development of GPU-accelerated technology, trading with machine learning algorithms has attracted the attention of many researchers and practitioners. In this research, we propose a novel…

Portfolio Management · Quantitative Finance 2021-03-23 Huanming Zhang , Zhengyong Jiang , Jionglong Su

We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology…

Methodology · Statistics 2019-02-06 Abhra Sarkar , David B. Dunson

Financial markets are complex adaptive systems characterized by collective behavior and abrupt regime shifts, particularly during crises. This paper studies time-varying dependencies in Nordic equity markets and examines whether…

Portfolio Management · Quantitative Finance 2026-01-13 Maksym A. Girnyk

The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…

Mathematical Finance · Quantitative Finance 2025-10-13 Nicola F. Zaugg , Lech A. Grzelak

This paper investigates portfolio selection within a continuous-time financial market with regime-switching and beliefs-dependent utilities. The market coefficients and the investor's utility function both depend on the market regime, which…

Optimization and Control · Mathematics 2024-10-23 Xiaochen Chen , Guohui Guan , Zongxia Liang

We propose a two-level, learning-based portfolio method (RL-BHRP) that spreads risk across sectors and stocks, and adjusts exposures as market conditions change. Using U.S. Equities from 2012 to mid-2025, we design the model using 2012 to…

Portfolio Management · Quantitative Finance 2025-08-19 Shaofeng Kang , Zeying Tian

Cryptocurrency markets exhibit pronounced momentum effects and regime-dependent volatility, presenting both opportunities and challenges for systematic trading strategies. We propose AdaptiveTrend, a multi-component algorithmic trading…

Computational Engineering, Finance, and Science · Computer Science 2026-02-13 Duc Bui , Thanh Nguyen

While investment funds publicly disclose their objectives in broad terms, their managers optimize for complex combinations of competing goals that go beyond simple risk-return trade-offs. Traditional approaches attempt to model this through…

Portfolio Management · Quantitative Finance 2025-10-31 Maarten P. Scholl , Mahmoud Mahfouz , Anisoara Calinescu , J. Doyne Farmer

Hidden Markov models (HMMs) are flexible time series models in which the distributions of the observations depend on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of…

Methodology · Statistics 2014-06-19 Roland Langrock , Thomas Kneib , Alexander Sohn , Stacy DeRuiter

Despite the empirical success of the rough Bergomi (rBergomi) model in modeling volatility dynamics, its practical use remains challenging due to high computational complexity in both pricing and calibration arising from its non-Markovian…

Computational Finance · Quantitative Finance 2026-04-09 Changqing Teng , Guanglian Li