arXiv subjects

Mark-Oliver Wolf

Publications and source records attributed to Mark-Oliver Wolf.

4 recordsLinked to original sources

arXiv2026

On the Estimation of Own Funds for Life Insurers: A Study of Direct, Indirect, and Control Variate Methods in a Risk-Neutral Pricing Framework

The Solvency Capital Requirement (SCR) calculation is computationally intensive, relying on the market-consistent estimation of own funds. While Solvency II prioritizes the direct valuation method, it theoretically yields the same value as the indirect method. This paper evaluates their practical performance within a risk-neutral pricing framework. First, we present a simplified proof that direct and indirect estimators converge to the same value. For $T$ being the number of time steps in the simulation, we then introduce a novel family of $2^T$ mixed estimators including both methods as edge cases, integrating them into a control variate framework for significant variance reduction. This framework is further extended to incorporate market frictions for real-world applicability. Evaluating these estimators on three life insurance asset-liability management models demonstrates that their performance is fundamentally driven by the degree of asset-liability coupling. While stronger coupling in realistic settings consistently favors the indirect method, neither baseline estimator is universally superior. Furthermore, this coupling directly impacts the success of our proposed control variates. They can dramatically reduce variance to one-tenth of the standard direct estimator, but their efficacy remains model-dependent. The source code is publicly available on https://gitlab.cc-asp.fraunhofer.de/itwm-fm-lv-public/wolf-estimation-of-own-funds.

q-fin.RM↗

arXiv2024

Application of ZX-calculus to Quantum Architecture Search

This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in Quantum Machine Learning (QML). Recognizing the challenges in designing efficient quantum circuits for QML, we propose a GP framework that utilizes mutations defined via ZX-calculus, a graphical language that can simplify visualizing and working with quantum circuits. Our methodology focuses on evolving quantum circuits with the aim of enhancing their capability to approximate functions relevant in various machine learning tasks. We introduce several mutation operators inspired by the transformation rules of ZX-calculus and investigate their impact on the learning efficiency and accuracy of quantum circuits. The empirical analysis involves a comparative study where these mutations are applied to a diverse set of quantum regression problems, measuring performance metrics such as the percentage of valid circuits after the mutation, improvement of the objective, as well as circuit depth and width. Our results indicate that certain ZX-calculus-based mutations perform significantly better than others for Quantum Architecture Search (QAS) in all metrics considered. They suggest that ZX-diagram based QAS results in shallower circuits and more uniformly allocated gates than crude genetic optimization based on the circuit model.

quant-ph↗

arXiv2023

Quantum Architecture Search for Quantum Monte Carlo Integration via Conditional Parameterized Circuits with Application to Finance

Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward approach based on pretraining parameterized quantum circuits, and show how they can be transformed into their conditional variant, making them usable as a subroutine in an AE algorithm. To identify a suitable circuit, we propose a genetic optimization approach that combines variable ansatzes and data encoding. We apply our algorithm to the problem of pricing financial derivatives. At the expense of a costly pretraining process, this results in a quantum circuit implementing the derivatives' payoff function more efficiently than previously existing quantum algorithms. In particular, we compare the performance for European vanilla and basket options.

quant-ph↗

arXiv2022

An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer

Modelling non-linear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating non-linearity in the form of the unit step function on a quantum computer. Our approach expands upon repeat-until-success protocols, suggesting a modification that requires a single measurement only. We describe two distinct circuit types which receive their input either directly from a classical computer, or as a quantum state when embedded in a more advanced quantum algorithm. All quantum circuits are theoretically evaluated using numerical simulation and executed on Noisy Intermediate-Scale Quantum hardware. We demonstrate that reliable experimental data with high precision can be obtained from our quantum circuits involving up to 8 qubits, and up to 25 CX-gate applications, enabled by state-of-the-art hardware-optimization techniques and measurement error mitigation.

quant-ph↗