Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
Study on hedging with delayed strategies for exponential utility maximization.
problem Maximizing exponential utility in semistatic hedging.
method Explicit computations for delayed semistatic hedging.
result Developed methods for hedging with delayed strategies.
Study develops efficient nested deep hedging method for derivatives pricing.
problem Hedging derivatives in market frictions using multiple options.
method Nested deep hedging approach with efficient learning techniques.
result Reduces arbitrage opportunities and improves hedging risks.
Model-free approach to hedge path-dependent options using min-max optimization.
problem Hedging path-dependent options with maturity T using a static portfolio of vanilla options.
method Model-free approach based on primal-dual Martingale Optimal Transport (MOT) problem, solving a min-max optimization problem.
result Provides theoretical bounds on hedging error at maturity T.
The paper addresses hedging Asian options with transaction costs using asymptotic hedging.
problem Hedging Asian options in markets with transaction costs.
method Asymptotic hedging approach.
result Probability convergence of investment portfolio value to payment function as revision count approaches infinity.
Hedging in the presence of transaction costs leads to complex optimization problems. These problems typically lack closed-form solutions, and their implementation relies on numerical methods that provide hedging strategies for specific parameter values. In this paper we use a genetic programming algorithm to derive exp…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be trea…
We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that the initial mean variance hedging problem is equivalent to a ne…
We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh and Naujokat and Westray, the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strat…
Deep Hedging learns optimal strategies for various risk levels.
problem Finding optimal hedging policies for diverse risk aversions.
method Continuous Reinforcement Learning with actor-critic algorithm.
result Demonstrated effectiveness in a stochastic volatility model.
The paper approximates financial derivatives using neural networks and iterated integrals.
problem Approximating p-integrable financial derivatives. method Using iterated Stratonovich integrals and neural networks.
result Approximate solutions to the Lp-hedging problem. Study tests if deep hedging differs from delta hedging in a GARCH market model.
problem Whether deep hedging includes speculative components in a GARCH market.
method Tested in a GARCH-based market model, comparing deep hedging and delta hedging.
result The difference between deep hedging and delta hedging is speculative if risk measure does not prioritize adverse outcomes.
The paper examines fair pricing and hedging stability under small numéraire perturbations.
problem Fair pricing and hedging stability under numéraire perturbations.
method Reformulating the stochastic control problem to show stability and deriving asymptotic formulas.
result Fair price and hedging strategy are stable with small numéraire perturbations.
The study designs a green investment fund and a hedging strategy for insurance policies linked to it.
problem Hedging unit-linked life insurance policies with an environmentally sensitive investment fund.
method Developed a carbon-intensity-driven portfolio selection rule and a quadratic hedging approach.
result The hedging strategy minimizes the variance of hedging costs, as demonstrated through numerical analysis.
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
A new algorithm for high-dimensional hedging problems.
problem High-dimensional, path-dependent hedging problems.
method Signature-based algorithm using operator-valued kernels and geometric rough paths.
result Theoretical guarantees on existence and uniqueness of a global minimum.
Second-order optimization speeds up deep hedging for complex options.
problem Hedging exotic options with market frictions in realistic markets.
method Second-order optimization scheme leveraging pathwise differentiability and Kronecker-factoring.
result Our method optimizes the policy in 1/4 the steps of standard optimization.
The paper finds optimal strategies for hedging in incomplete markets using derivatives.
problem Optimal static hedging in incomplete markets with two underlying assets and vanilla options.
method Formulated as a utility maximization problem, solved through variational methods and fixed point analysis.
result Semi-analytical solutions for exponential, power/logarithmic, and quadratic utilities, with convergence to a fixed point for exponential utility.
Hedge has been proposed as an adaptive scheme, which guides an agent's decision in resource selection and distribution problems that can be modeled as a multi-armed bandit full information game. Such problems are encountered in the areas of computer and communication networks, e.g. network path selection, load distribu…
We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.
Proposes a deep hedging method for robust pricing and hedging under parameter uncertainty.
problem Pricing and hedging under parameter uncertainty for generalized affine processes.
method Deep learning approach linked to variational form of Kolmogorov equation.
result Robust deep hedging outperforms existing methods in volatile periods.
We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance-optimality and provide tractable formulas u…
Optimal hedging strategy found in markets with incomplete pricing kernels.
problem Finding optimal hedging in markets with incomplete pricing kernels.
method Demonstrated existence of an optimal hedge portfolio using an expected least squared-error criterion.
result Existence of an optimal hedge portfolio in Lévy-Ito markets.
This report was originally written as an industry white paper on Hedge Funds. This paper gives an overview to Hedge Funds, with a focus on risk management issues. We define and explain the general characteristics of Hedge Funds, their main investment strategies and the risk models employed. We address the problems in H…
Deep learning solves high-dimensional quadratic hedging problems.
problem High-dimensional incomplete markets with mean-variance and local risk minimization.
method Deep learning-based BSDE solver for optimal hedging strategies.
result High-dimensional quadratic hedging is efficiently computed with deep learning.
The paper solves a utility-based hedging problem with quadratic costs.
problem Optimal trading strategy for hedging European contingent claims with quadratic transaction costs.
method Duality theory applied to exponential utility maximization problem.
result Explicit computation of optimal trading strategy for quadratic payoffs.
Deep Bellman Hedging uses reinforcement learning to optimize financial portfolio hedging.
problem Optimizing financial portfolio hedging with derivatives and trading frictions.
method Actor-critic reinforcement learning algorithm with continuous state and action spaces.
result Trained model provides optimal hedge for any initial portfolio and market state.
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options with discrete set of maturities but a continuum of strikes. In …
The paper compares traditional regression with modern neural network methods for financial hedging and risk compression.
problem Finding optimal hedge ratios and managing portfolio risk using traditional regression methods has limitations.
method The paper introduces regularization techniques and common factor analyses using neural networks to improve upon regression methods.
result Neural network methods provide better performance in hedge ratio estimation and risk compression compared to traditional regression.
In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert advice, is surprisingly both worst-case optimal and adaptive to the easier stochastic …
This paper compares eight DRL algorithms for dynamic hedging.
problem Optimal dynamic hedging strategies using Deep Reinforcement Learning.
method Eight DRL algorithms (MCPG, PPO, DQL, DDPG) compared using a GJR-GARCH(1,1) simulated dataset.
result MCPG and PPO outperform the Black-Scholes delta hedge baseline.
We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itō calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategie…
Enhances hedging strategies using deep neural networks.
problem Optimizing risks and returns in financial hedging.
method Integrates deep neural networks and random forest classifiers to find optimal hedging strategies.
result Improved hedging strategies with lower costs and risks.
RL and DTSOC for final quadratic hedging performance studied.
problem Optimal hedging of European call options with and without transaction costs.
method Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control.
result RL and DTSOC perform similarly to variance-optimal hedging in various market models.
A new DRL model optimizes hedging with market impact for low-liquidity stocks.
problem Optimizing hedging strategies for stocks with limited liquidity.
method Integrates Deep Reinforcement Learning with realistic market impact features.
result Optimal hedging policies learned from DRL model perform better in low-liquidity scenarios.
New algorithm reduces training time for deep learning in financial hedging.
problem Optimal hedging in markets with transaction costs.
method ST-Hedging algorithm combining deep learning and FBSDE solver.
result Achieves state-of-the-art performance and scalability.
Risk-averse reinforcement learning optimizes option hedging.
problem Optimizing option hedging under risk aversion and realistic market conditions.
method Applied Trust Region Volatility Optimization (TRVO) to a vanilla option hedging environment.
result The derived hedging strategy outperforms Black & Scholes and is robust to market variations.
Study optimizes Bitcoin futures hedging to reduce liquidation risk.
problem Optimizing hedging strategies to minimize liquidation risk in Bitcoin futures.
method Derived a semi-closed form optimal hedging strategy considering spot and futures extreme returns, loss aversion, leverage, and collateral management.
result Optimal strategy reduces both hedged portfolio variance and liquidation probability.
This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomp…
New dual approach for hedging Bermudan options efficiently.
problem Computing efficient hedging portfolios for Bermudan options.
method Pure dual approach, rewriting dual pricing formula as excess reward representation, strict convexification, Monte Carlo method.
result Convergence and effectiveness of the new algorithm tested on various Bermudan options.
Study scaling limits for option pricing in trinomial models.
problem Analyzing exponential hedging in trinomial models converging to Black-Scholes.
method Purely probabilistic approach using duality, martingale, and weak-convergence techniques.
result Derives a scaling limit for exponential certainty-equivalent prices in trinomial models.
Optimal hedging framework with variational preferences under convex risk measures.
problem Optimal hedging with variational preferences under convex risk measures.
method Theoretical hedging optimization framework with dual representation of risk measures and utilities.
result Derivation of optimality and indifference pricing conditions.
We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential…
Framework for robust control under model uncertainty, improving financial derivatives hedging.
problem Model uncertainty in financial derivatives hedging.
method Dynamic programming principle for solving one-step optimization problems.
result Robust hedging strategy outperforms model-based strategies during adverse scenarios.
Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that UCB, M3, S or Exp3 algorithms have good behaviours on average in RMG. Besides, hedging algorithms have been shown to be effective on predi…
Monte Carlo Tree Search improves financial derivative hedging efficiency.
problem Optimizing pricing and hedging of derivative contracts in incomplete markets.
method Integrates tree search techniques with Reinforcement Learning for optimal control problems.
result Monte Carlo Tree Search outperforms Q-learning in sample efficiency and learning speed. The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literatures treat the MVH problem by the duality method, here we study a system consisting of three BSDEs derived b…
This paper solves hedging in incomplete markets using neural networks.
problem Hedging in incomplete markets with risk factor, illiquidity, and discrete transaction dates.
method Proposes a jump-diffusion model and uses RNN, LSTM, and Mogrifier-LSTM neural networks for hedging strategies.
result Mogrifier-LSTM is the fastest and most effective model for hedging.