Computational Finance and Risk Analysis in Insurance II

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 11789

Special Issue Editor


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Guest Editor
1. Department of Mathematics, TU Kaiserslautern, Erwin Schrödinger Strasse, Geb. 48, 67653 Kaiserslautern, Germany
2. Department Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
Interests: portfolio optimization; stochastic control in finance and insurance; risk-return assessment to financial products; Monte Carlo simulation; tree methods; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Whilst developing valuation concepts for financial products, modelling of financial processes, risk measurement issues and portfolio optimization are often central aspects of research, the computational methods to produce the final numbers are equally important in the application of financial and insurance mathematics.

With this Special Issue I would like to encourage all colleagues (from both academia and industry) working in the computational area of finance and insurance to share their innovative methods with the community. These methods can be (but are not limited to) the following:

  • variants of classical computational approaches such as Monte Carlo algorithms, tree methods, quadrature or methods to solve partial differential equations,
  • new machine learning methods, in particular neural network approaches,
  • algorithms from computational statistics,
  • specialized algorithms to deal with an important practical issue.

The Special Issue favours contributions that are closely related to a specific application in real life, but also theoretical contributions that e.g. deal with the convergence or speed up of well-established methods are welcome. Survey papers on areas of computational finance might also be acceptable, but should only be handed in after having contacted me.

Prof. Dr. Ralf Korn
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Monte Carlo methods
  • tree methods and algorithms for PDE related to finance/insurance
  • risk assessment
  • machine learning methods
  • neural networks

Published Papers (5 papers)

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Research

17 pages, 482 KiB  
Article
Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization
by Ivica Turkalj, Mohammad Assadsolimani, Markus Braun, Pascal Halffmann, Niklas Hegemann, Sven Kerstan, Janik Maciejewski, Shivam Sharma and Yuanheng Zhou
Risks 2024, 12(2), 23; https://doi.org/10.3390/risks12020023 - 29 Jan 2024
Viewed by 1502
Abstract
In this paper, we consider the inclusion of the solvency capital requirement (SCR) into portfolio optimization by the use of a quadratic proxy model. The Solvency II directive requires insurance companies to calculate their SCR based on the complete loss distribution for the [...] Read more.
In this paper, we consider the inclusion of the solvency capital requirement (SCR) into portfolio optimization by the use of a quadratic proxy model. The Solvency II directive requires insurance companies to calculate their SCR based on the complete loss distribution for the upcoming year. Since this task is, in general, computationally challenging for insurance companies (and therefore, not taken into account during portfolio optimization), employing more feasible proxy models provides a potential solution to this computational difficulty. Here, we present an approach that is also suitable for future applications in quantum computing. We analyze the approximability of the solvency capital ratio in a quadratic form using machine learning techniques. This allows for an easier consideration of the SCR in the classical mean-variance analysis. In addition, it allows the problem to be formulated as a quadratic unconstrained binary optimization (QUBO), which benefits from the potential speedup of quantum computing. We provide a detailed description of our model and the translation into a QUBO. Furthermore, we investigate the performance of our approach through experimental studies. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance II)
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26 pages, 1195 KiB  
Article
Estimating the Value-at-Risk by Temporal VAE
by Robert Buch, Stefanie Grimm, Ralf Korn and Ivo Richert
Risks 2023, 11(5), 79; https://doi.org/10.3390/risks11050079 - 23 Apr 2023
Cited by 2 | Viewed by 1945
Abstract
Estimation of the value-at-risk (VaR) of a large portfolio of assets is an important task for financial institutions. As the joint log-returns of asset prices can often be projected to a latent space of a much smaller dimension, the use of a variational [...] Read more.
Estimation of the value-at-risk (VaR) of a large portfolio of assets is an important task for financial institutions. As the joint log-returns of asset prices can often be projected to a latent space of a much smaller dimension, the use of a variational autoencoder (VAE) for estimating the VaR is a natural suggestion. To ensure the bottleneck structure of autoencoders when learning sequential data, we use a temporal VAE (TempVAE) that avoids the use of an autoregressive structure for the observation variables. However, the low signal-to-noise ratio of financial data in combination with the auto-pruning property of a VAE typically makes use of a VAE prone to posterior collapse. Therefore, we use annealing of the regularization to mitigate this effect. As a result, the auto-pruning of the TempVAE works properly, which also leads to excellent estimation results for the VaR that beat classical GARCH-type, multivariate versions of GARCH and historical simulation approaches when applied to real data. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance II)
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33 pages, 570 KiB  
Article
The Convergence Rate of Option Prices in Trinomial Trees
by Guillaume Leduc and Kenneth Palmer
Risks 2023, 11(3), 52; https://doi.org/10.3390/risks11030052 - 06 Mar 2023
Cited by 1 | Viewed by 3150
Abstract
We study the convergence of the binomial, trinomial, and more generally m-nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for [...] Read more.
We study the convergence of the binomial, trinomial, and more generally m-nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the coefficients of 1/n and 1/n in the expansion of the error for digital and standard put and call options. This result is obtained from an Edgeworth series in the form of Kolassa–McCullagh, which we derive from a recently established Edgeworth series in the form of Esseen/Bhattacharya and Rao for triangular arrays of random variables. We apply our result to the most popular trinomial trees and provide numerical illustrations. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance II)
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25 pages, 1604 KiB  
Article
Supervised Machine Learning Classification for Short Straddles on the S&P500
by Alexander Brunhuemer, Lukas Larcher, Philipp Seidl, Sascha Desmettre, Johannes Kofler and Gerhard Larcher
Risks 2022, 10(12), 235; https://doi.org/10.3390/risks10120235 - 09 Dec 2022
Cited by 1 | Viewed by 1953
Abstract
In this paper, we apply machine learning models to execute certain short-option strategies on the S&P500. In particular, we formulate and focus on a supervised classification task which decides if a plain short straddle on the S&P500 should be executed or not on [...] Read more.
In this paper, we apply machine learning models to execute certain short-option strategies on the S&P500. In particular, we formulate and focus on a supervised classification task which decides if a plain short straddle on the S&P500 should be executed or not on a daily basis. We describe our used framework and present an overview of our evaluation metrics for different classification models. Using standard machine learning techniques and systematic hyperparameter search, we find statistically significant advantages if the gradient tree boosting algorithm is used, compared to a simple “trade always” strategy. On the basis of this work, we have laid the foundations for the application of supervised classification methods to more general derivative trading strategies. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance II)
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14 pages, 766 KiB  
Article
A Quantum Algorithm for Pricing Asian Options on Valuation Trees
by Mark-Oliver Wolf, Roman Horsky and Jonas Koppe
Risks 2022, 10(12), 221; https://doi.org/10.3390/risks10120221 - 22 Nov 2022
Cited by 1 | Viewed by 1987
Abstract
We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load [...] Read more.
We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load the corresponding distribution onto the states. We implement the expectation value of the option pricing formula as a composition of the price probabilities, the payout and an indicator function, mapping their respective values to amplitudes of additional qubits. Thus, the underlying no longer has to be discretized into the same bit values for different times, resulting in smaller quantum circuits. The algorithm may be used with quantum amplitude estimation, enabling a quadratic speed-up over classical Monte Carlo methods. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance II)
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