English
Related papers

Related papers: Markov Decision Processes under Model Uncertainty

200 papers

We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observer. In addition, while the state process and the controls are…

Optimization and Control · Mathematics 2022-06-22 Tomasz R. Bielecki , Igor Cialenco , Andrzej Ruszczyński

In this paper we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic to tackle…

Optimization and Control · Mathematics 2020-09-10 Tomasz R. Bielecki , Tao Chen , Igor Cialenco

We study infinite-horizon robust Markov decision processes (MDPs) on continuous state spaces with structured rectangular ambiguity set. The proposed ambiguity set falls within the convex hull of unknown generating kernels. We utilize the…

Optimization and Control · Mathematics 2026-05-28 Mengmeng Li , Yifan Hu , Daniel Kuhn , Yan Li

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…

Computational Finance · Quantitative Finance 2025-06-10 Hans Buehler , Blanka Horvath , Yannick Limmer , Thorsten Schmidt

Many real-world decision-making problems involve multiple decision-making stages and various objectives. Besides, most of the decisions need to be made before having complete knowledge about all aspects of the problem leaves some sort of…

Optimization and Control · Mathematics 2025-08-06 Babooshka Shavazipour , Theodor J. Stewart

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…

Optimization and Control · Mathematics 2022-09-20 Francesco Micheli , Tyler Summers , John Lygeros

We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…

Systems and Control · Computer Science 2014-06-04 Krishnamurthy Dvijotham , Maryam Fazel , Emanuel Todorov

This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the…

Optimization and Control · Mathematics 2020-08-31 Qi Zhang , Wei Feng

Portfolio optimization has been a major topic of research in finance, as it has a significant impact on investment profit. In this paper, we investigate the problem of data uncertainty in convex multi-objective portfolio optimization. We…

Optimization and Control · Mathematics 2018-04-11 Amin Mohazab Rahimzadeh , Alireza Saranj

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…

Optimization and Control · Mathematics 2020-06-16 Johannes Wiebe , Inês Cecílio , Jonathan Dunlop , Ruth Misener

This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…

Mathematical Finance · Quantitative Finance 2019-09-09 Benjamin James Duthie

This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at…

Portfolio Management · Quantitative Finance 2016-02-03 Rüdiger Frey , Abdelali Gabih , Ralf Wunderlich

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…

Artificial Intelligence · Computer Science 2017-10-26 Dimitri Scheftelowitsch , Peter Buchholz , Vahid Hashemi , Holger Hermanns

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…

Pricing of Securities · Quantitative Finance 2024-04-11 Felix L. Wolf , Griselda Deelstra , Lech A. Grzelak

Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In robust MDP (RMDP), every action is associated with an uncertainty set of probability distributions, modelling…

Artificial Intelligence · Computer Science 2024-12-16 Tobias Meggendorfer , Maximilian Weininger , Patrick Wienhöft

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…

Mathematical Finance · Quantitative Finance 2021-07-15 Yu-Jui Huang , Xiang Yu

In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…

Optimization and Control · Mathematics 2025-09-04 Siyu Lv , Zhen Wu , Jie Xiong , Xin Zhang

We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as…

Risk Management · Quantitative Finance 2021-11-30 Eva Lütkebohmert , Thorsten Schmidt , Julian Sester

This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…

Optimization and Control · Mathematics 2023-03-08 Diego Fonseca , Mauricio Junca

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

Optimization and Control · Mathematics 2015-01-07 Pengyu Qian , Zizhuo Wang , Zaiwen Wen