Robust Risk-Aware Option Hedging

This paper presents a methodology for the design of adaptive control systems using multiple controllers which can control an unknown plant whose parameters change widely. It is not necessary to estimate the plant parameter values in our system. Multiple controllers are constructed by several basic controllers. Switching from the current basic controller to a more appropriate one is based on one-way simple switching rules. The switching rules only utilize the information of whether the control has succeeded or failed. We introduce the control and robust performance criteria. The former is used to produce a number of candidates for the basic controllers for typical plant models. The latter is used to select several basic controllers from the candidates to construct multiple controllers in order to achieve the system robust performance. To illustrate the effectiveness of the approach, we apply the control system to the cart-pole problem with changeable length of the pole.

This paper reviews 17 studies addressing dynamic option hedging in frictional markets through Deep Reinforcement Learning (DRL). Specifically, this work analyzes the DRL models, state and action spaces, reward formulations, data generation processes and results for each study. It is found that policy methods such as DDPG are more commonly employed due to their suitability for continuous action spaces. Despite diverse state space definitions, a lack of consensus exists on variable inclusion, prompting a call for thorough sensitivity analyses. Mean-variance metrics prevail in reward formulations, with episodic return, VaR and CvaR also yielding comparable results. Geometric Brownian motion is the primary data generation process, supplemented by stochastic volatility models like SABR (stochastic alpha, beta, rho) and the Heston model. RL agents, particularly those monitoring transaction costs, consistently outperform the Black–Scholes Delta method in frictional environments. Although consistent results emerge under constant and stochastic volatility scenarios, variations arise when employing real data. The lack of a standardized testing dataset or universal benchmark in the RL hedging space makes it difficult to compare results across different studies. A recommended future direction for this work is an implementation of DRL for hedging American options and an investigation of how DRL performs compared to other numerical American option hedging methods.

Static Hedging of Standard Options

A novel engineering approach for assessing the robustness of fuzzy logic control (FLC) systems with modified parallel distributed compensation (MPDC) is presented. It addresses the problem of successful implementation and operation in industrial environment of designed systems for the control of complex plants with model uncertainty. The research steps on modified Takagi–Sugeno–Kang (MTSK) plant models MTSKn and MTSKlow already derived and validated for normal and low plant loads from experimental data for the level of the solution in an industrial carbonisation column for soda ash production. MPDC with PI linear local controllers are developed based on the MTSKn plant model, which differ in the parameters that are optimised by genetic algorithms for fitness functions with and without robustness requirements and different random initial parameter values. The MTSKn and each of the designed MPDC are represented according to suggested criteria by a nominal and varied linear plant model and controller, respectively. Then, robust stability and robust performance criteria are derived for the linearised MPDC–MTSKn systems. The system performance and robustness are investigated in the frequency domain and from the simulated reference step responses for MTSKn and MTSKlow, with the results benchmarked against an existing adaptive FLC.

05/02514 A robust damping controller for SMES using loop-shaping technique

Local Risk Minimization on Supply Curve Model with Market Impacts

In this paper, we consider problems of hedging path-dependent basket barrier options using individual options based on our previously proposed optimal hedging strategy in Yamada (2010-2013) for European options. The optimal hedging problem is formulated as follows: Find optimal smooth functions of individual options to minimize the mean square error from the payoff of down-and-out basket option. For solving the problem, we first express the necessary and sufficient condition in terms of linear equations regarding conditional expectations of basket barrier options. Based on the Brownian bridge decomposition and the Independence Lemma, we show that the computations involving conditional expectations of basket barrier options may be reduced to those of unconditional expectations. This computation involves multiple integrations in general, but is usually executed efficiently based on the standard Monte Carlo method by generating independent Gaussian random numbers. Finally, we demonstrate numerical experiments to illustrate our proposed methodology.

If the market is incomplete, we have several choices of equivalent martingale measures to price contingent claims .Recall that we didn't impose conditions on the preferences of the economic agents other than that they prefer more to less. So it is quite natural to specify the preferences further in order to select one of the equivalent martingale measures.The specification of the investor's attitude towards risk is done in terms of a utility function. Credit risk is increasingly being recognised as a significant area of risk and arbitrage, yet there exists relatively little research on it. In this paper we show that operational risk represents a fundamental risk to option hedging (1) and investigate it by proposing a new theoretical model. We derive an exposure indicator for the operational risk of option hedging and the resulting operational risk distribution. We obtain analytical results for various risk measures including the Value at Risk equation; this includes deriving a new analytical result for the option function of the half-normal distributions (which will be of interest to Statisticians in general). We determine an analytical solution to the price of options under operational risk (2). We conduct numerical experiments on empirical option data to validate our model and estimate the operational Value at Risk for option hedging. There exists currently a good deal of literature on hedging methods for the pricing options. It is well known that in this case a straightforward Monte Carlo simulation algorithm will be time-consuming and yield unstable results for the prices and especially the sensitivities. The knock-in/out features in the barrier option payoffs lead to slower convergence of the Monte Carlo algorithm. To address this problem the following (semi-)analytical approaches have been developed for specific models. In any case, theoretically, long-run uncertainty about demographic changes and shocks restricts the land supply and raises the land price. The consequences for housingpolicies may be significant, especially in countries (likeFrance) where policymakers attempt to develop the housingstock and to make housing more affordable for the less well-off. Now, the spatial demographic risk is local by nature: a shortfall in one place entails a surplus somewhere else; therefore, it is an insurable risk. Consequently, a future insurance market may be a tool with which to improve the way the housing market works. Empirically, we conduct the analysis for a French department, Nord. The data base used in this study is made up of individual transactions for developable land for residential purposes(19,495observations) or secondary or tertiary activities (1,667 observations) between 1989 and 2002.The results show that, during the upward trend in the land market, the price of developable land is significantly higher when the change in population in the vicinity is more volatile, and so more difficult to predict. The plot price is 7.8% (housing market) or 15.3% (office and factory market) higher when population change in the 10 nearest communes increases by one standard deviation. 2. A General Option-Pricing Formula we compare our results with those given by Merton (3).We first explain Merton's results. Merton restricted his discussion to discrete probability distributions. Let an asset have terminal value

To obtain propellant formulations with superior comprehensive and robustness performance, the study establishes a multi-objective optimization model that accounts for uncertainties. The model adopts a bi-layer structure. The inner layer computes performance bounds to construct uncertainty intervals, which are subsequently transformed into deterministic performance via interval order relations. The outer layer optimizes component mass fractions using MOEA/D (Multi-objective Evolutionary Algorithm Based on Decomposition) to maximize the deterministic performance. The study leverages Large Language Models (LLMs) as pre-trained optimizers to automate the operator design of MOEA/D. Designers can identify formulations that satisfy the performance requirements and robustness criteria by adjusting uncertainty levels and MOEA/D weight coefficients. The results on ZDTs and UFs demonstrate that MOEA/D-LLM achieves approximately a 4.0% improvement in hypervolume values compared to MOEA/D. Additionally, the NEPE propellant optimization case shows that MOEA/D-LLM improves the computational speed by about 13.05% and enhances hypervolume values by around 2.7% compared to MOEA/D. The specific impulse increases by 1.11%, the generation of aluminum oxide and hydrogen chloride decreases by approximately 18.43% and 16.40%, respectively, and the impact sensitivity is reduced by about 1.67%.

On reset option pricing in binomial market with both fixed and proportional transaction costs

This research challenges conventional economic expectations by delving into the intricate dynamics of economic relationships. Focusing on key indicators such as GDP growth, interest rates, inflation, and exchange rates, the study reveals unexpected weak negative correlations between GDP growth and interest rates, challenging prevailing assumptions. Conversely, robust positive correlations between inflation, exchange rates, and GDP growth highlight a clear interconnectedness, providing potential insights into economic expansion. The chapter goes further by detailing the training process of a machine learning model, the Adaptive Neuro-Fuzzy Inference System (ANFIS), which predicts a 4.2225% GDP growth in 2024 after 10 epochs. Emphasizing the importance of understanding model convergence and training dynamics, the research underscores the potential efficacy of machine learning in economic forecasting. ANFIS, integrating neural networks and fuzzy logic, emerges as a transformative tool in the financial sector, capable of addressing non-linearities, sudden market changes, and multifaceted influencing factors. Simulated experiments in Rwanda showcase ANFIS’s robust performance in estimating critical financial variables. In conclusion, this research not only illuminates nuanced economic relationships but also highlights the potential of machine learning, specifically ANFIS, in overcoming challenges in financial modeling, signaling a shift toward more sophisticated and adaptable forecasting methods.

Simple SummaryThis research explores the potential of machine learning (ML) to predict late-stage colorectal cancer (CRC) diagnoses. The focus is on understanding how socioeconomic and regional factors affect cancer care, particularly in detecting CRC at an advanced stage. We aim to merge data on social determinants of health with individual demographics to uncover patterns indicating higher CRC risk. We compared various ML models, such as decision trees, random forest, and gradient boosting to find the most effective tool for this task. The goal is to utilize artificial intelligence (AI) for early, more accurate CRC detection, which can lead to better treatment outcomes. This study promises to significantly contribute to cancer research, potentially leading to more personalized and efficient healthcare strategies that could ultimately save lives.Purpose: To assess the efficacy of various machine learning (ML) algorithms in predicting late-stage colorectal cancer (CRC) diagnoses against the backdrop of socio-economic and regional healthcare disparities. Methods: An innovative theoretical framework was developed to integrate individual- and census tract-level social determinants of health (SDOH) with sociodemographic factors. A comparative analysis of the ML models was conducted using key performance metrics such as AUC-ROC to evaluate their predictive accuracy. Spatio-temporal analysis was used to identify disparities in late-stage CRC diagnosis probabilities. Results: Gradient boosting emerged as the superior model, with the top predictors for late-stage CRC diagnosis being anatomic site, year of diagnosis, age, proximity to superfund sites, and primary payer. Spatio-temporal clusters highlighted geographic areas with a statistically significant high probability of late-stage diagnoses, emphasizing the need for targeted healthcare interventions. Conclusions: This research underlines the potential of ML in enhancing the prognostic predictions in oncology, particularly in CRC. The gradient boosting model, with its robust performance, holds promise for deployment in healthcare systems to aid early detection and formulate localized cancer prevention strategies. The study’s methodology demonstrates a significant step toward utilizing AI in public health to mitigate disparities and improve cancer care outcomes.

The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chemical space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of organic molecules. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single molecules or materials, while remaining applicable to the general class of organic molecules composed of the elements CHNO.

This paper proposes an accelerated static replication approach for continuous European‐style barrier options by employing the repeated Richardson extrapolation technique with the Romberg sequence. This approach is developed under the constant elasticity of variance (CEV) model of Cox (1975) and Cox and Ross (1976) using the framework offered by Derman, Ergener, and Kani (1995; DEK) and its modified method of Chung et al. (2010, 2013a, 2013b) and Tsai (2014). The numerical results indicate that our method could significantly reduce replication errors for European knock‐out call options and may be superior to the imposition of the theta‐matching condition on the DEK method.

The pricing and static hedging of multi-step double barrier options