Model stock price dynamics using semi-Markov processes.
problem Model stock price dynamics through a semi-Markov process.
method Use semi-Markov process with Poisson random measure, establish existence and uniqueness of solution, derive HJB equation.
result Obtain expressions for optimal controls and value function using HJB equation.
Machine learning infers time-reversible dynamics from data.
problem Learn time-reversible dynamics constrained by initial and final conditions.
method Machine learning algorithms solve boundary value problems for deterministic and stochastic dynamics.
result Inferred time-reversible dynamics for various types of systems.
The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
problem Defining and analyzing set-valued stochastic integrals for Lévy processes.
method Extending classical definitions to convoluted integrals with square-integrable kernels, and proving properties of set-valued convoluted stochastic integrals.
result Set-valued convoluted stochastic integrals can be explosive and take extended vector values.
Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.
problem Investigates set-valued risk measures for processes and vectors.
method Utilizes equivalence of risk measures for processes and vectors and their penalty function formulations.
result Provides new dual representation for risk measures for processes in the set-valued framework.
Develops a dynamic mean field theory for reinforcement learning.
problem Finite state and action Bayesian reinforcement learning in large state spaces.
method Analogies with statistical physics, interpreting probabilities as couplings and values as spins, solving mean field equations.
result State-action values are statistically independent in the asymptotic state space limit, with exact or approximate equations for computation.
Study on measure-valued CARMA processes in Banach spaces.
problem Modeling dynamics of functionals of spatio-temporal random fields.
method Defined measure-valued CARMA processes and derived conditions for stationarity.
result Positive measure-valued CARMA processes can model spatio-temporal random fields.
Model predicts depegging dynamics of stablecoins like Tether and Bitcoin.
problem Understanding depegging effects of stablecoins on cryptocurrencies.
method Multivariate Hawkes process model.
result Numerical example shows model's effectiveness.
Ensemble method for fast portfolio valuation and risk management.
problem Dynamic portfolio valuation and risk management from cash flow data.
method Regression trees for dynamic value process learning.
result Fast and accurate estimator with closed-form solution.
Study values American passport options in an exponential Lévy model.
problem Valuing an exotic derivative called the American passport option.
method Derived pricing equation using dynamic programming principle and proved viscosity solution.
result Option value is a viscosity solution of variational inequality and is convex.
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, x(t), depends on the stochasticity of the return on investment, r(t), for which different model assumptions are discussed. The fat-tail d…
We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel.…
Improved meta-learning for dynamics using additional structured knowledge.
problem Meta-learning for dynamics with limited raw observations.
method Extended Neural ODE Process model to use privileged information.
result Improved accuracy and calibration on simulated dynamics tasks.
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximiz…
A new model captures forward curve dynamics with stochastic volatility.
problem Modeling continuous-time evolution of forward curves in financial markets.
method Affine stochastic volatility model with modulated dynamics.
result Model allows for maturity-specific risk and volatility clustering.
We develop a new DTSM with nonlinearities using Gaussian Processes for better interest rate forecasting.
problem Linear DTSMs fail to capture nonlinear relationships between macroeconomic variables and interest rates.
method We propose a Gaussian Process-based sequential Monte Carlo estimation and forecasting scheme.
result Nonlinear models outperform linear ones in forecasting core inflation, leading to significant economic value gains.
New method for optimistic planning in MDPs using regularization.
problem Optimistic planning in infinite-horizon discounted MDPs.
method Regularized dynamic programming for approximate value iteration.
result Achieves near-optimal statistical guarantees in learning policies.
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert space…
A new algorithm uses IVs to learn optimal policies from observational data.
problem Learning optimal policies from unobserved variable confounded data.
method IV-aided Value Iteration (IVVI) algorithm based on conditional moment restrictions.
result First provably efficient algorithm for instrument-aided offline RL.
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…
Paper proposes a method to estimate multiple dynamic quantiles jointly.
problem Limited joint estimation of multiple dynamic quantiles.
method Introduces a crossing penalty objective function for joint estimation.
result Validation through Monte Carlo experiments and empirical application on FTSE100 shows effectiveness.
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values …
This paper defines systematic value investing as an empirical optimization problem. Predictive modeling is introduced as a systematic value investing methodology with dynamic and optimization features. A predictive modeling process is demonstrated using financial metrics from Gray & Carlisle and Buffett & Clark. A 31-y…
We study the forward price dynamics in commodity markets realized as a process with values in a Hilbert space of absolutely continuous functions defined by Filipović. The forward dynamics are defined as the mild solution of a certain stochastic partial differential equation driven by an infinite dimensional Lévy proces…
We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled …
Paper approximates solutions for complex decision processes with limited precision.
problem Approximating the set of all solutions for Multi-objective Markov Decision Processes.
method Limited precision approach based on White's multi-objective value-iteration dynamic programming algorithm.
result The number of calculated solutions is tractable and approximates the true Pareto front.
Investigates price dynamics of two assets with and without bubbles, deriving conditions for equilibrium prices.
problem Understanding price dynamics and bubbles in multi-asset markets.
method Derives sufficient and necessary conditions for average equilibrium price dynamics in a two-asset model.
result Assets with positive average dividends display hump-shaped bubbles, while those with constant fundamental values show misvaluation effects.
UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.
problem Improving value function learning in complex reinforcement learning tasks.
method Uncertainty-aware low-rank Q-matrix estimation (UA-LQE) algorithm.
result UA-LQE selectively erases uncertain entries in Q-matrix to improve value function approximation.
Study uses viscosity solutions to solve control problems involving measure-valued martingales.
problem Stochastic control problems with measure-valued martingale state processes.
method Viscosity solution approach exploiting structural properties of MVM processes.
result Value function is the unique viscosity solution to the HJB equation.
In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a c…
Efficiently processes dynamic inputs in AI writing assistants with incremental computation.
problem Efficiently updating AI models in real-time with dynamic inputs.
method Incremental computing using vector quantization to filter and reuse intermediate values in neural networks.
result Comparable accuracy with 12.1X fewer operations for processing dynamic inputs.
We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we redu…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an R+-valued best bid price process and an Lloc2-valued volume process. …
Improves predictions by integrating forward-looking views into dynamic factor models.
problem Poor forecasts from historical data when dynamics change.
method Combines historical data with forward-looking views using a dynamic factor model.
result Derives optimal portfolio strategies influenced by both myopic and intertemporal factors.
The paper values perpetual callable American volatility options using a mean-reverting volatility model.
problem Valuation of callable American volatility put options.
method Modeling volatility dynamics as a mean-reverting 3/2 process and proposing a pricing formula.
result The value of perpetual callable American volatility put options is discussed under given conditions.
Improves reinforcement learning agent's scene-specific value function.
problem High variance in samples for policy gradient computations in multi-scene environments.
method Proposes dynamic value estimation (DVE) for multiple MDPs, clustering value functions across scenes.
result Lower sample variance and more accurate scene-specific value function estimates.
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Here we use phylogenetic Gaussian process regression to model the evolution of simulated function-valued traits. Given function-valued data only from the tips of an evolutionary tree and utilising independent pri…
Paper proposes a new framework for robust multi-modal data fusion under uncertainty.
problem Unexpected modality failures in nonlinear non-Gaussian dynamic processes.
method Dynamic model averaging (DMA) based particle filter (PF) algorithm.
result The proposed solution outperforms state-of-the-art methods in experiments.
DEMOTE uses neural diffusion-reaction processes to capture temporal dynamics in sparse tensor data.
problem Sparse and temporally associated tensor data with limited structural knowledge.
method Develops a neural diffusion-reaction process to estimate dynamic embeddings for tensor modes.
result Captures both commonalities and personalities in evolving tensor entries.
In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes {S(n)}n=0∞ to a limit process S we prove convergence Dynkin's games values corresponding to {S(n)}n=0∞ to the Dynkin's game…
Proposes a new model to better handle overdispersed count time series.
problem Heterogeneous overdispersed count time series.
method Negative-Binomial Randomized Gamma Markov Process.
result Significantly improves predictive performance and fast convergence of inference algorithm.
We characterize value functions in partially observable MDPs as semi-algebraic sets.
problem Understanding feasible value functions in partially observable Markov decision processes.
method Characterization of feasible value functions as semi-algebraic sets defined by polynomial inequalities.
result The feasible set of value functions in POMDPs is a semi-algebraic set, not a polytope as in MDPs.
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price process is driven by Brownian motion, an associated "master equation" for the dynam…
Proposes dynamic channel pruning during neural network training.
problem Pruning neural networks during training to reduce computational cost and improve efficiency.
method Dynamic channel propagation to update channel utility values and selectively prune channels.
result Our scheme trains and prunes neural networks simultaneously, achieving superior performance.
Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
problem Whether 2-valued dynamics can be defined by the action of a 2-valued group.
method Construction of examples of dynamics that are or are not group actions.
result Some 2-valued dynamics on complex plane cannot be defined by the action of a 2-valued group.
Time-variant value function transfer method for RL.
problem Transfer learning with time-variant task distributions.
method Variational approach leveraging temporal structure.
result The proposed method outperforms time-invariant approach in experiments.
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processe…
This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity n…
Study on reinforcement learning dynamics using statistical physics.
problem Understanding how reinforcement learning dynamics interact with parameters and state features.
method Statistical physics concepts applied to temporal difference learning with linear function approximators.
result Stochastic semi-gradient noise leads to significant plateaus in value error.