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Julian Sester

Publications and source records attributed to Julian Sester.

At least 19 recordsLinked to original sources
arXiv2026

Robustness in Sequential Decision Making under Evolving Uncertainty: Evidence from High-Frequency Market Making

We study sequential decision making under evolving uncertainty in high-frequency financial markets, where changing market dynamics continually challenge static decision policies. We show that robustness has two economically meaningful dimensions: uncertainty tolerance, which determines how much uncertainty the decision maker allows, and action robustness, which governs how conservatively decisions respond. Robustness is not merely protection against model misspecification, but a state-dependent mechanism that reshapes sequential decision behaviors. Simulation and empirical evidence show that action robustness has a substantially larger impact than uncertainty tolerance. Moreover, excessive robustness may reduce profitability in illiquid markets by limiting execution opportunities.

q-fin.TR↗
arXiv2025

Fast catastrophe bond valuation with neural-network surrogates

Catastrophe bonds are increasingly important risk-transfer securities, but structural pricing is too slow for real-time valuation, screening, and sensitivity analysis. We develop a neural-network surrogate for the pricing operator of a compound-Poisson catastrophe bond model. Training labels are generated by Monte Carlo simulation with importance sampling, so the network learns variance-reduced structural prices rather than sparse market quotes which are difficult to extrapolate reliably. Across Gamma and Lognormal severity specifications, the selected networks attain very small absolute approximation error on the stated training domain. After training, 1000 contracts are priced in about 0.03--0.04 seconds, compared with tens to hundreds of seconds for Monte Carlo with importance sampling and many hours for a partial integro-differential equation benchmark. The result is a fast in-domain structural valuation engine that also produces economically interpretable sensitivities to catastrophe intensity, attachment threshold, and interest rates.

q-fin.PR↗
arXiv2025

Empirical Analysis of the Model-Free Valuation Approach: Hedging Gaps, Conservatism, and Trading Opportunities

In this paper we study the quality of model-free valuation approaches for financial derivatives by systematically evaluating the difference between model-free super-hedging strategies and the realized payoff of financial derivatives using historical option prices from several constituents of the S&P 500 between 2018 and 2022. Our study allows in particular to describe the realized gap between payoff and model-free hedging strategy empirically so that we can quantify to which degree model-free approaches are overly conservative. Our results imply that the model-free hedging approach is only marginally more conservative than industry-standard models such as the Heston-model while being model-free at the same time. This finding, its statistical description and the model-independence of the hedging approach enable us to construct an explicit trading strategy which, as we demonstrate, can be profitably applied in financial markets, and additionally possesses the desirable feature with an explicit control of its downside risk due to its model-free construction preventing losses pathwise.

q-fin.PR↗
arXiv2025

Distributionally Robust Deep Q-Learning

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.

cs.LG↗
arXiv2024

Generative modelling of financial time series with structured noise and MMD-based signature learning

Generating synthetic financial time series data that accurately reflects real-world market dynamics holds tremendous potential for various applications, including portfolio optimization, risk management, and large scale machine learning. We present an approach that {uses structured noise} for training generative models for financial time series. The expressive power of the signature transform {has been shown to be able} to capture the complex dependencies and temporal structures inherent in financial data {when used to train generative models in the form of a signature kernel }. We employ a moving average model to model the variance of the noise input, enhancing the model's ability to reproduce stylized facts such as volatility clustering. Through empirical experiments on S\&P 500 index data, we demonstrate that our model effectively captures key characteristics of financial time series and outperforms comparable {approaches}. In addition, we explore the application of the synthetic data generated to train a reinforcement learning agent for portfolio management, achieving promising results. Finally, we propose a method to add robustness to the generative model by tweaking the noise input so that the generated sequences can be adjusted to different market environments with minimal data.

q-fin.MF↗
arXiv2024

Q-Learning under Finite Model Uncertainty

We propose a robust Q-learning algorithm for Markov decision processes under model uncertainty when each state-action pair is associated with a finite ambiguity set of candidate transition kernels. This finite-measure framework enables highly flexible, user-designed uncertainty models and goes beyond the common KL and Wasserstein ball formulations. We establish almost sure convergence of the learned Q-function to the robust optimum, and derive non-asymptotic high-probability error bounds that separate stochastic approximation error from transition-kernel estimation error. Finally, we show that Wasserstein ball and parametric ambiguity sets can be approximated by finite ambiguity sets, allowing our algorithm to be used as a generic solver beyond the finite setting.

math.OC↗
arXiv2024

Non-concave stochastic optimal control in finite discrete time under model uncertainty

In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent ambiguity sets of probability measures comprising, as a natural example, the ambiguity set defined via Wasserstein-balls around path-dependent reference measures with path-dependent radii, as well as parametric classes of probability distributions. We establish a dynamic programming principle which allows to derive both optimal control and worst-case measure by solving recursively a sequence of one-step optimization problems. Moreover, we derive upper bounds for the difference of the values of the robust and non-robust stochastic control problem in the Wasserstein uncertainty and parameter uncertainty case. As a concrete application, we study the robust hedging problem of financial derivatives under an asymmetric (and non-convex) loss function accounting for different preferences of sell- and buy side when it comes to the hedging of financial derivatives. As our entirely data-driven ambiguity set of probability measures, we consider Wasserstein-balls around the empirical measure derived from real financial data. We demonstrate that during adverse scenarios such as a financial crisis, our robust approach outperforms typical model-based hedging strategies such as the classical Delta-hedging strategy as well as the hedging strategy obtained in the non-robust setting with respect to the empirical measure and therefore overcomes the problem of model misspecification in such critical periods.

math.OC↗
arXiv2024

Measuring Name Concentrations through Deep Learning

We propose a new deep learning approach for the quantification of name concentration risk in loan portfolios. Our approach is tailored for small portfolios and allows for both an actuarial as well as a mark-to-market definition of loss. The training of our neural network relies on Monte Carlo simulations with importance sampling which we explicitly formulate for the CreditRisk${+}$ and the ratings-based CreditMetrics model. Numerical results based on simulated as well as real data demonstrate the accuracy of our new approach and its superior performance compared to existing analytical methods for assessing name concentration risk in small and concentrated portfolios.

q-fin.RM↗
arXiv2023

On the Relevance and Appropriateness of Name Concentration Risk Adjustments for Portfolios of Multilateral Development Banks

Sovereign loan portfolios of Multilateral Development Banks (MDBs) typically consist of only a small number of borrowers and hence are heavily exposed to single name concentration risk. Based on realistic MDB portfolios constructed from publicly available data, this paper quantifies the magnitude of the exposure to name concentration risk using exact Monte Carlo simulations. In comparing the exact adjustment for name concentration risk to its analytic approximation as currently applied by the major rating agency Standard & Poor's, we further investigate whether current capital adequacy frameworks for MDBs are overly conservative. Finally, we discuss the choice of appropriate model parameters and their impact on measures of name concentration risk.

q-fin.RM↗
arXiv2023

Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems

In this note we provide an upper bound for the difference between the value function of a distributionally robust Markov decision problem and the value function of a non-robust Markov decision problem, where the ambiguity set of probability kernels of the distributionally robust Markov decision process is described by a Wasserstein-ball around some reference kernel whereas the non-robust Markov decision process behaves according to a fixed probability kernel contained in the ambiguity set. Our derived upper bound for the difference between the value functions is dimension-free and depends linearly on the radius of the Wasserstein-ball.

math.OC↗
arXiv2023

On intermediate Marginals in Martingale Optimal Transportation

We study the influence of additional intermediate marginal distributions on the value of the martingale optimal transport problem. From a financial point of view, this corresponds to taking into account call option prices not only, as usual, for those call options where the respective future maturities coincide with the maturities of some exotic derivative but also additional maturities and then to study the effect on model-independent price bounds for the exotic derivative. We characterize market settings, i.e., combinations of the payoff of exotic derivatives, call option prices and marginal distributions that guarantee improved price bounds as well as those market settings that exclude any improvement. Eventually, we showcase in numerous examples that the consideration of additional price information on vanilla options may have a considerable impact on the resultant model-independent price bounds.

q-fin.MF↗
arXiv2023

Neural networks can detect model-free static arbitrage strategies

In this paper we demonstrate both theoretically as well as numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some. Due to the use of neural networks, our method can be applied to financial markets with a high number of traded securities and ensures almost immediate execution of the corresponding trading strategies. To demonstrate its tractability, effectiveness, and robustness we provide examples using real financial data. From a technical point of view, we prove that a single neural network can approximately solve a class of convex semi-infinite programs, which is the key result in order to derive our theoretical results that neural networks can detect model-free static arbitrage strategies whenever the financial market admits such opportunities.

q-fin.CP↗
arXiv2022

Robust $Q$-learning Algorithm for Markov Decision Processes under Wasserstein Uncertainty

We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball around a (possibly estimated) reference measure. We prove convergence of the presented algorithm and provide several examples also using real data to illustrate both the tractability of our algorithm as well as the benefits of considering distributional robustness when solving stochastic optimal control problems, in particular when the estimated distributions turn out to be misspecified in practice.

cs.LG↗
arXiv2022

Markov Decision Processes under Model Uncertainty

We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.

math.OC↗
arXiv2022

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

We show how inter-asset dependence information derived from market prices of options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the traded option, we either extract correlation information or we derive restrictions on the set of admissible copulas that capture the inter-asset dependencies. To compute the resultant price bounds for some multi-asset options of interest, we apply a modified martingale optimal transport approach. Several examples based on simulated and real market data illustrate the improvement of the obtained price bounds and thus provide evidence for the relevance and tractability of our approach.

q-fin.MF↗
arXiv2022

Detecting data-driven robust statistical arbitrage strategies with deep neural networks

We present an approach, based on deep neural networks, that allows identifying robust statistical arbitrage strategies in financial markets. Robust statistical arbitrage strategies refer to trading strategies that enable profitable trading under model ambiguity. The presented novel methodology allows to consider a large amount of underlying securities simultaneously and does not depend on the identification of cointegrated pairs of assets, hence it is applicable on high-dimensional financial markets or in markets where classical pairs trading approaches fail. Moreover, we provide a method to build an ambiguity set of admissible probability measures that can be derived from observed market data. Thus, the approach can be considered as being model-free and entirely data-driven. We showcase the applicability of our method by providing empirical investigations with highly profitable trading performances even in 50 dimensions, during financial crises, and when the cointegration relationship between asset pairs stops to persist.

q-fin.CP↗
arXiv2021

Robust deep hedging

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 special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework. The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches, in particular in highly volatile periods.

q-fin.RM↗