arXiv research

Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.

Paper introduces PRMs to learn non-Markovian stochastic rewards for reinforcement learning.

Unified analytical tool for non-Markovian jump processes.

Analyzes non-Markovian environments in stochastic approximation.

Paper tackles robust offline RL for non-Markovian processes, improving efficiency and applicability.

Paper improves neural ODEs for forecasting non-Markovian processes.

Deep learning solves non-Markovian FBSDEs for utility maximization.

We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This val…

FLDD improves discrete diffusion models by learning a non-Markovian noising process.

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…

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…

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show t…

The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.

Study develops numerical schemes for non-Markovian volatility models with memory.

ARL bridges non-Markovian decision processes with reinforcement learning, improving foresight and stability.

New model controls memory in seq2seq tasks, revealing learning regimes.

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…

Using a relationship between the moments of the probability distribution of times between the two consecutive trades (intertrade time distribution) and the moments of the distribution of a daily number of trades we show, that the underlying point process generating times of the trades is an essentially non-markovian lo…

Path signatures improve hedging of exotic derivatives in non-Markovian models.

Study proves value of non-Markovian games with partial, asymmetric info.

Representation learning on networks offers a powerful alternative to the oft painstaking process of manual feature engineering, and as a result, has enjoyed considerable success in recent years. However, all the existing representation learning methods are based on the first-order network (FON), that is, the network th…

A new macroscopic market making model connects market making and optimal execution.

In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão, Ohashi and Russo and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartinga…

The paper values variable annuities using complex stochastic models and deep learning.

Develops non-Markovian couplings for sub-Riemannian Brownian motions.

Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.

Efficient RL in PRMs with improved regret bound.

Develops RL algorithm for non-Markovian, non-stationary reward streams.

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…

Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.

New method for pricing European options in rough LSV models.

Two signature-based methods solve optimal stopping in non-Markovian frameworks.

FinFlowRL learns from experts to optimize financial control in changing markets.

Paper solves complex game theory problems with new equations.

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…

Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.

We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal contro…

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…

Next-gen reservoir computers fail to predict complex processes, highlighting need for better architectures.

Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we…

Study online learning of quantum processes, showing feasibility for certain types.

Study analyzes non-Markovian effects in financial markets over multiple years.

Transformers can solve complex filtering problems for non-Gaussian signals.

Paper tackles non-Markovian control problems with new learning methods.

Exact asymptotic solutions found for nonlinear Hawkes processes.

DBIMs speed up DDBMs and improve image translation.

This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve the portfolio optimization problem with the martingale optimality principle. Optim…

FDBM models use fractional Brownian motion to model complex stochastic processes.