Model Uncertainty

Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling ArXiv ID: 2506.07299 “View on arXiv” Authors: Hans Buehler, Blanka Horvath, Yannick Limmer, Thorsten Schmidt Abstract 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 unavailability of the true probability measure forces reliance on an empirical approximation, and even small misestimations can lead to significant deviations in decision quality. Building on the framework of Klibanoff et al. (2005), we enhance the conventional objective - whether this is expected utility in an investing context or a hedging metric - by superimposing an outer “uncertainty measure”, motivated by traditional monetary risk measures, on the space of models. In scenarios where a natural model distribution is lacking or Bayesian methods are impractical, we propose an ad hoc subsampling strategy, analogous to bootstrapping in statistical finance and related to mini-batch sampling in deep learning, to approximate model uncertainty. To address the quadratic memory demands of naive implementations, we also present an adapted stochastic gradient descent algorithm that enables efficient parallelization. Through analytical, simulated, and empirical studies - including multi-period, real data and high-dimensional examples - we demonstrate that uncertainty measures outperform traditional mixture of measures strategies and our model-agnostic subsampling-based approach not only enhances robustness against model risk but also achieves performance comparable to more elaborate Bayesian methods. ...

Distributionally Robust Deep Q-Learning ArXiv ID: 2505.19058 “View on arXiv” Authors: Chung I Lu, Julian Sester, Aijia Zhang Abstract We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The uncertainty is taken into account by considering the worst-case transition from a ball around a reference probability measure. To determine the optimal policy under the worst-case state transition, we solve the associated non-linear Bellman equation by dualising and regularising the Bellman operator with the Sinkhorn distance, which is then parameterized with deep neural networks. This approach allows us to modify the Deep Q-Network algorithm to optimise for the worst case state transition. We illustrate the tractability and effectiveness of our approach through several applications, including a portfolio optimisation task based on S&{“P”}~500 data. ...

Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach ArXiv ID: 2410.01378 “View on arXiv” Authors: Unknown Abstract This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {“Therein, w”}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {“analysis”} for forward investment and consumption under model uncertainty. ...

Deep Gamma Hedging ArXiv ID: 2409.13567 “View on arXiv” Authors: Unknown Abstract We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black–Scholes model then we find the network will successfully learn the Black-Scholes gamma hedging strategy, even if the dynamics of the underlying do not match the Black–Scholes model, so long as we choose a loss function that rewards coping with model uncertainty. Our results suggest that the reason gamma hedging is used in practice is to account for model uncertainty rather than to reduce the impact of transaction costs. ...

Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment ArXiv ID: 2407.02831 “View on arXiv” Authors: Unknown Abstract We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to robustness captured by the homothetic multiplier robust specification, and the investor’s investment and consumption strategies are constrained to closed convex sets. To solve this constrained robust control problem, we employ the stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory. Furthermore, we show the investor incurs (non-negative) utility loss, i.e. the loss in welfare, if model uncertainty is ignored. When the model coefficients are deterministic, we establish formally the relationship between the investor’s robustness preference and the robust optimal investment-consumption strategy and the value function, and the impact of investment and consumption constraints on the investor’s robust optimal investment-consumption strategy and value function. Extensive numerical experiments highlight the significant impact of ambiguity aversion, consumption and investment constraints, on the investor’s robust optimal investment-consumption strategy, utility loss, and value function. Key findings include: 1) short-selling restriction always reduces the investor’s utility loss when model uncertainty is ignored; 2) the effect of consumption constraints on utility loss is more delicate and relies on the investor’s risk aversion level. ...

Predictive Decision Synthesis for Portfolios: Betting on Better Models ArXiv ID: 2405.01598 “View on arXiv” Authors: Unknown Abstract We discuss and develop Bayesian dynamic modelling and predictive decision synthesis for portfolio analysis. The context involves model uncertainty with a set of candidate models for financial time series with main foci in sequential learning, forecasting, and recursive decisions for portfolio reinvestments. The foundational perspective of Bayesian predictive decision synthesis (BPDS) defines novel, operational analysis and resulting predictive and decision outcomes. A detailed case study of BPDS in financial forecasting of international exchange rate time series and portfolio rebalancing, with resulting BPDS-based decision outcomes compared to traditional Bayesian analysis, exemplifies and highlights the practical advances achievable under the expanded, subjective Bayesian approach that BPDS defines. ...

A Framework for Treating Model Uncertainty in the Asset Liability Management Problem ArXiv ID: 2310.11987 “View on arXiv” Authors: Unknown Abstract The problem of asset liability management (ALM) is a classic problem of the financial mathematics and of great interest for the banking institutions and insurance companies. Several formulations of this problem under various model settings have been studied under the Mean-Variance (MV) principle perspective. In this paper, the ALM problem is revisited under the context of model uncertainty in the one-stage framework. In practice, uncertainty issues appear to several aspects of the problem, e.g. liability process characteristics, market conditions, inflation rates, inside information effects, etc. A framework relying on the notion of the Wasserstein barycenter is presented which is able to treat robustly this type of ambiguities by appropriate handling the various information sources (models) and appropriately reformulating the relevant decision making problem. The proposed framework can be applied to a number of different model settings leading to the selection of investment portfolios that remain robust to the various uncertainties appearing in the market. The paper is concluded with a numerical experiment for a static version of the ALM problem, employing standard modelling approaches, illustrating the capabilities of the proposed method with very satisfactory results in retrieving the true optimal strategy even in high noise cases. ...