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In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…

Risk Management · Quantitative Finance 2021-02-01 Suman Thapa , Yiqiang Q. Zhao

This paper studies a Value-at-Risk (VaR)-regulated optimal portfolio problem of the equity holders of a participating life insurance contract. In a setting with unhedgeable mortality risk and complete financial market, the optimal solution…

Mathematical Finance · Quantitative Finance 2020-11-17 Thai Nguyen , Mitja Stadje

RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow…

Machine Learning · Computer Science 2025-09-30 Haoran He , Yuxiao Ye , Qingpeng Cai , Chen Hu , Binxing Jiao , Daxin Jiang , Ling Pan

Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…

Logic in Computer Science · Computer Science 2018-04-16 Tim Quatmann , Joost-Pieter Katoen

The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…

Pricing of Securities · Quantitative Finance 2012-04-17 Adi Ben-Meir , Jeremy Schiff

After several years of development, the Solvency II-project has finally been set to work in the European Union with the beginning of the year 2016. This has caused massive changes in the regional legislative supervisory acts. One new aspect…

Applications · Statistics 2020-12-17 Dietmar Pfeifer

Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…

Statistics Theory · Mathematics 2020-03-09 Robert Yuen , Stilian Stoev , Dan Cooley

In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…

Computational Finance · Quantitative Finance 2022-09-30 Devang Sinha , Siddhartha P. Chakrabarty

The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in…

Computational Finance · Quantitative Finance 2021-07-26 Alexandre Carbonneau , Frédéric Godin

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial…

Computational Finance · Quantitative Finance 2024-06-07 T. van der Zwaard , L. A. Grzelak , C. W. Oosterlee

This paper presents a novel two-stage optimization framework designed to model integrated quantile functions, which leads to the formulation of a bilinear optimization problem (P). A specific instance of this framework offers a new approach…

Optimization and Control · Mathematics 2025-12-01 Ashish Chandra , Mohit Tawarmalani

The right ventricular (RV) function deterioration strongly predicts clinical outcomes in numerous circumstances. To boost the clinical deployment of ensemble regression methods that quantify RV volumes using tabular data from the widely…

Tissues and Organs · Quantitative Biology 2024-03-13 Tuan A. Bohoran , Polydoros N. Kampaktsis , Laura McLaughlin , Jay Leb , Gerry P. McCann , Archontis Giannakidis

A promising way to improve the sample efficiency of reinforcement learning is model-based methods, in which many explorations and evaluations can happen in the learned models to save real-world samples. However, when the learned model has a…

Machine Learning · Computer Science 2022-09-14 Haoxin Lin , Yihao Sun , Jiaji Zhang , Yang Yu

In reinforcement learning, two objective functions have been developed extensively in the literature: discounted and averaged rewards. The generalization to an entropy-regularized setting has led to improved robustness and exploration for…

Machine Learning · Computer Science 2025-01-20 Jacob Adamczyk , Volodymyr Makarenko , Stas Tiomkin , Rahul V. Kulkarni

Within the Own Risk and Solvency Assessment framework, the Solvency II directive introduces the need for insurance undertakings to have efficient tools enabling the companies to assess the continuous compliance with regulatory solvency…

Risk Management · Quantitative Finance 2013-12-24 Julien Vedani , Fabien Ramaharobandro

In practice, the value-at-risk (VaR) for a longer holding period is often scaled using the 'square root of time rule'. The VaR is determined for a shorter holding period and then scaled up according to the desired holding period. For…

Risk Management · Quantitative Finance 2022-05-05 Marita Kuhlmann

This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin…

Mathematical Finance · Quantitative Finance 2021-03-31 Guusje Delsing , Michel Mandjes , Peter Spreij , Erik Winands

The largest US banks are required by regulatory mandate to estimate the operational risk capital they must hold using an Advanced Measurement Approach (AMA) as defined by the Basel II/III Accords. Most use the Loss Distribution Approach…

Risk Management · Quantitative Finance 2014-12-01 J. D. Opdyke

Value-at-Risk (VaR) and Expected Shortfall (ES) are widely used in the financial sector to measure the market risk and manage the extreme market movement. The recent link between the quantile score function and the Asymmetric Laplace…

Machine Learning · Statistics 2021-05-14 Zhengkun Li , Minh-Ngoc Tran , Chao Wang , Richard Gerlach , Junbin Gao

This paper extends the utility maximization literature by combining partial information and (robust) regulatory constraints. Partial information is characterized by the fact that the stock price itself is observable by the optimizing…

Risk Management · Quantitative Finance 2025-09-23 Nicole Bäuerle , An Chen