Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
problem Optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
method Martingale optimal principle and quadratic BSDEs with exponential moment.
result Establishes optimal strategies for consumption and investment.
Study analyzes non-Markovian effects in financial markets over multiple years.
problem Understanding non-Markovian dynamics and trader interactions in financial markets.
method Empirical analysis of self-response functions and trade sign correlators for different stocks over multiple years.
result Significant variations in traders' interactions over time, indicating changes in market mechanisms.
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
FinFlowRL learns from experts to optimize financial control in changing markets.
problem Traditional finance control methods fail in real-world, non-stationary markets.
method Imitation-Reinforcement Learning framework that pretrains on expert strategies and finetunes in noise space.
result Consistently outperforms individually optimized experts across diverse market conditions.
A new macroscopic market making model connects market making and optimal execution.
problem Connecting market making and optimal execution problems.
method Using continuous processes for orders, the model bridges the gap between market making and optimal execution.
result Demonstrates the model's effectiveness through various noise and intensity function scenarios.
Signature portfolios approximate optimal wealth in non-Markovian markets.
problem Approximating optimal wealth in non-Markovian markets.
method Linear path-functional portfolios based on signatures of market weights.
result Signature portfolios can uniformly approximate any continuous portfolio function.
Novel signature approach for pricing and hedging path-dependent options with market frictions.
problem Pricing and hedging path-dependent options with market frictions.
method Signature approach, mean-quadratic variation criterion, non-standard infinite-dimensional Riccati equations, time-augmented signature, non-Markovian stochastic control problem.
result Effective hedging strategies in frictional markets with low-truncated signature approximations.
This paper studies the equilibrium pricing of asset shares in the presence of dynamic private information. The market consists of a risk-neutral informed agent who observes the firm value, noise traders, and competitive market makers who set share prices using the total order flow as a noisy signal of the insider's inf…
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
Market making is one of the most important aspects of algorithmic trading, and it has been studied quite extensively from a theoretical point of view. The practical implementation of so-called "optimal strategies" however suffers from the failure of most order book models to faithfully reproduce the behaviour of real m…
In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic partial differential inequality; this is determined entirely on the basis of th…
Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.
problem Understanding the scaling behavior of non-Markovian point processes.
method Analyzed a confined fractional Brownian motion-driven point process and compared it to a nonlinear Markovian process.
result A nonlinear Markovian process can reproduce the power-law scaling behavior of a non-Markovian point process.
Investigates mean-variance portfolio selection in non-Markovian markets.
problem Continuous-time Markowitz mean-variance portfolio selection in fake stationary affine Volterra models.
method Stochastic factor solution to a Riccati BSDE, deriving explicit solutions as multi-dimensional Riccati-Volterra equations.
result Analytical closed-form expressions for optimal portfolio policies and mean-variance efficient frontier.
Paper solves complex game theory problems with new equations.
problem Zero-sum stochastic games with non-Markovian switching.
method New multidimensional SRE and BSDE solutions.
result Existence and uniqueness of SRE solutions.
Paper introduces PRMs to learn non-Markovian stochastic rewards for reinforcement learning.
problem Lack of structured representation for non-Markovian stochastic rewards in reinforcement learning.
method Introduces probabilistic reward machines (PRMs) and presents an algorithm to learn them from decision processes.
result Algorithm proves correct and convergent for learning PRMs from decision processes.
A new model predicts price concavity and reversion after metaorder execution.
problem Modeling market response to exogenous trades on limit order books.
method Developed a Non-Markovian Zero Intelligence model with a time-weighted mid-price return function.
result The model predicts concave price paths and price reversion after metaorder execution.
Deep learning solves non-Markovian FBSDEs for utility maximization.
problem Solving utility maximization problems under rough volatility.
method Deep learning-based numerical methods for non-Markovian fully coupled FBSDEs.
result Error estimates and convergence provided for the deep learning approach.
We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the super-replication cost in these models are obtained and used to prove the limit the…
Paper uses DDPG to learn optimal execution strategies in dynamic markets.
problem Learning non-Markovian optimal execution strategies in dynamic financial markets.
method Introduces a novel actor-critic algorithm based on DDPG for transient price impact modeling.
result Successfully approximates optimal execution strategy through numerical experiments.
Paper tackles robust offline RL for non-Markovian processes, improving efficiency and applicability.
problem Learning robust policies for non-Markovian decision processes with limited offline data.
method Proposes a novel algorithm with dataset distillation and LCB design for robust values, derived new dual forms, and introduces concentrability coefficients.
result Proves polynomial sample efficiency for finding ε-optimal robust policies.
FinFlowRL combines imitation and reinforcement learning for better financial control.
problem Traditional stochastic control methods fail in real-world finance due to changing market conditions.
method FinFlowRL uses imitation learning to pretrain an adaptive meta policy, then finetunes it with reinforcement learning.
result FinFlowRL consistently outperforms individual strategies across various market conditions.
It is shown how the generating functional method of De Dominicis can be used to solve the dynamics of the original version of the minority game (MG), in which agents observe real as opposed to fake market histories. Here one again finds exact closed equations for correlation and response functions, but now these are de…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our re…
A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.
problem Distinguishing between sequences with different correlation degrees.
method Minimum relative entropy principle applied to cluster partitions of power-law correlated sequences.
result Optimal Hurst exponents are selected for market price series, indicating non-markovianity.
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predi…
Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probabi…
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single s…
Unified analytical tool for non-Markovian jump processes.
problem Analyzing history-dependent jump processes with non-Markovian behavior.
method Developed a standard form of master equations using Laplace-space embedding and asymptotic solution.
result Unified analytical toolset for general non-Markovian processes, leading to the GLE approximation.
Two signature-based methods solve optimal stopping in non-Markovian frameworks.
problem Optimal stopping in non-Markovian frameworks, particularly pricing American options.
method Primal and dual formulations using linear functionals of rough path signatures.
result Both primal and dual methods converge and provide numerical examples.
Study utility maximization with delayed information in continuous time Gaussian markets.
problem Maximizing utility with delayed information in continuous time Gaussian markets.
method Purely probabilistic approach based on Radon-Nikodym derivatives of Gaussian measures.
result Solution for optimal control and value in a specific Gaussian framework.
The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.
problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.
Study develops numerical schemes for non-Markovian volatility models with memory.
problem Existence and uniqueness of strong solutions for non-Markovian SDEs.
method Functional quantization scheme based on Lamperti transformation.
result Theoretical foundation for numerical schemes applied to specific models.
The dynamical behavior of the currency exchange rate after its large-scale catastrophe is discussed through a case study of the rate of Russian rubles to US dollars after its crash in 2014. It is shown that, similarly to the case of the stock market crash, the relaxation is characterized by a power law, which is in ana…
Motivated by the asset-liability management of a nuclear power plant operator, we consider the problem of finding the least expensive portfolio, which outperforms a given set of stochastic benchmarks. For a specified loss function, the expected shortfall with respect to each of the benchmarks weighted by this loss func…
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct ε-optimal stopping tim…
This study examines memory effects in S&P500 market correlations using Langevin models.
problem The neglect of memory effects in market correlations for optimal portfolio selection.
method Fit a generalised Langevin equation (GLE) to S&P500 market correlation data.
result Memory effects in market correlations significantly improve forecasting accuracy and suggest a hidden slow time scale.
In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class o…
Paper improves neural ODEs for forecasting non-Markovian processes.
problem Forecasting irregularly observed time series with incomplete data.
method Path-dependent Neural Jump ODEs with signature transform.
result Path-dependent NJ-ODE outperforms original framework in non-Markovian data.
Paper tackles non-Markovian control problems with new learning methods.
problem Non-Markovian stochastic control problems with unknown parameters.
method Off-model training and importance sampling for deep neural network approximation.
result Quantitative error bounds for adaptive learning under model uncertainty.
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is…
New method identifies precursors of financial crises in market correlation structures.
problem Predicting long-term financial crises in non-Markovian, non-stationary markets.
method Identifying quasi-stationary market states and their precursor properties.
result Certain features of market states show potential as indicators of financial crises.
DeepSynth synthesizes automata to guide deep RL agents through sparse, non-Markovian rewards.
problem Training deep RL agents with sparse, non-Markovian rewards and unknown high-level objectives.
method Employing a novel algorithm for synthesizing compact automata to uncover sequential structure from trace data.
result Reduces the number of iterations required for policy synthesis by two orders of magnitude and improves scalability.
This paper studies a class of non−Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a Z−constrained BSDE, with dynamics associated to a non singular underlying forward process. Du…
Study pricing derivatives in markets with long-range dependence and jumps.
problem Deriving pricing formulas for derivatives in markets with long-range dependence and jumps.
method Developed a fractional integro-partial differential equation (PIDE) and used semigroup theory and finite-difference schemes for numerical solutions.
result Closed-form pricing formula for European options and numerical solution for general options.
Paper introduces MVS to detect non-Markovian observations in reinforcement learning.
problem Real-world sensors violate Markov property, leading to suboptimal reinforcement learning performance.
method Uses prediction-based Markov Violation Score (MVS) combining random forest and ridge regression.
result MVS detects non-Markovian structure in observation trajectories, quantifying its impact.
We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among different financial markets. The delay phenomenon can be recognized as the integral ty…
Path signatures improve hedging of exotic derivatives in non-Markovian models.
problem Hedging exotic derivatives under non-Markovian stochastic volatility models.
method Investigates path signatures in deep and shallow learning contexts, comparing neural networks and regression approaches.
result Path signatures outperform LSTM in most cases and yield more accurate results in hedging.
Extends pricing methods for index options under rough volatility.
problem Pricing and hedging of index options under non-Markovian dynamics.
method Extension of large deviations methods to non-local volatility dynamics, specifically rough volatility.
result Validates the approach for pricing index options under rough volatility.