A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new method predicts non-Markovian closure terms for complex systems.
problem Predicting the effect of unresolved variables on resolved dynamics in high-dimensional systems.
method Mamba-Assisted Closure (MAC) framework: sequence model trained to predict closure from resolved trajectory, coupled with reduced-order equations.
result Substantially outperforms existing methods in predictive accuracy and long-time stability.
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this work, we present a framework of operator inference to extract the governing dynamic…
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.
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 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.
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 revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a Lévy process Z extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a dual variational problem as it is customarily done for non-Markovian models. One of …
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…
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…
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…
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…
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…
We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial quandles coincide, we give a simple description of this closure operator, and analy…
The study connects lamination and orbit closures in hyperbolic manifolds.
problem Understanding the geometric and dynamical properties of horocycle orbit closures in Z-covers of compact hyperbolic manifolds.
method Exposes connections between distance minimizing laminations and horospherical orbit closures in Z-covers of compact hyperbolic manifolds. Provides novel constructions and explicit descriptions.
result Even slight perturbations to hyperbolic metrics can drastically change horocycle orbit closures.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
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…