Conditional Value-at-Risk

Robust MCVaR Portfolio Optimization with Ellipsoidal Support and Reproducing Kernel Hilbert Space-based Uncertainty ArXiv ID: 2509.00447 “View on arXiv” Authors: Rupendra Yadav, Aparna Mehra Abstract This study introduces a portfolio optimization framework to minimize mixed conditional value at risk (MCVaR), incorporating a chance constraint on expected returns and limiting the number of assets via cardinality constraints. A robust MCVaR model is presented, which presumes ellipsoidal support for random returns without assuming any distribution. The model utilizes an uncertainty set grounded in a reproducing kernel Hilbert space (RKHS) to manage the chance constraint, resulting in a simplified second-order cone programming (SOCP) formulation. The performance of the robust model is tested on datasets from six distinct financial markets. The outcomes of comprehensive experiments indicate that the robust model surpasses the nominal model, market portfolio, and equal-weight portfolio with higher expected returns, lower risk metrics, enhanced reward-risk ratios, and a better value of Jensen’s alpha in many cases. Furthermore, we aim to validate the robust models in different market phases (bullish, bearish, and neutral). The robust model shows a distinct advantage in bear markets, providing better risk protection against adverse conditions. In contrast, its performance in bullish and neutral phases is somewhat similar to that of the nominal model. The robust model appears effective in volatile markets, although further research is necessary to comprehend its performance across different market conditions. ...

FinRL-DeepSeek: LLM-Infused Risk-Sensitive Reinforcement Learning for Trading Agents ArXiv ID: 2502.07393 “View on arXiv” Authors: Unknown Abstract This paper presents a novel risk-sensitive trading agent combining reinforcement learning and large language models (LLMs). We extend the Conditional Value-at-Risk Proximal Policy Optimization (CPPO) algorithm, by adding risk assessment and trading recommendation signals generated by a LLM from financial news. Our approach is backtested on the Nasdaq-100 index benchmark, using financial news data from the FNSPID dataset and the DeepSeek V3, Qwen 2.5 and Llama 3.3 language models. The code, data, and trading agents are available at: https://github.com/benstaf/FinRL_DeepSeek ...

Sample Average Approximation for Portfolio Optimization under CVaR constraint in an (re)insurance context ArXiv ID: 2410.10239 “View on arXiv” Authors: Unknown Abstract We consider optimal allocation problems with Conditional Value-At-Risk (CVaR) constraint. We prove, under very mild assumptions, the convergence of the Sample Average Approximation method (SAA) applied to this problem, and we also exhibit a convergence rate and discuss the uniqueness of the solution. These results give (re)insurers a practical solution to portfolio optimization under market regulatory constraints, i.e. a certain level of risk. ...

Quantum Risk Analysis of Financial Derivatives ArXiv ID: 2404.10088 “View on arXiv” Authors: Unknown Abstract We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative pricing, and the second based on a novel approach using Quantum Signal Processing (QSP). Previous work in the literature has shown that quantum advantage is possible in the context of individual derivative pricing and that advantage can be leveraged in a straightforward manner in the estimation of the VaR and CVaR. The algorithms we introduce in this work aim to provide an additional advantage by encoding the derivative price over multiple market scenarios in superposition and computing the desired values by applying appropriate transformations to the quantum system. We perform complexity and error analysis of both algorithms, and show that while the two algorithms have the same asymptotic scaling the QSP-based approach requires significantly fewer quantum resources for the same target accuracy. Additionally, by numerically simulating both quantum and classical VaR algorithms, we demonstrate that the quantum algorithm can extract additional advantage from a quantum computer compared to individual derivative pricing. Specifically, we show that under certain conditions VaR estimation can lower the latest published estimates of the logical clock rate required for quantum advantage in derivative pricing by up to $\sim 30$x. In light of these results, we are encouraged that our formulation of derivative pricing in the QSP framework may be further leveraged for quantum advantage in other relevant financial applications, and that quantum computers could be harnessed more efficiently by considering problems in the financial sector at a higher level. ...