New method uses PDMPs with sub-sampling for efficient sampling from posterior distributions.
problem Efficient sampling from posterior distributions with limited data access.
method Approximate simulation of PDMPs with sub-sampling and stochastic gradient estimation.
result Stochastic-gradient PDMPs are efficient and robust compared to Langevin dynamics.
Improved PDMP samplers for multi-modal distributions using tempering.
problem Struggles of PDMP samplers with multi-modal or heavy-tailed distributions.
method Tempering PDMPs by interpolating between a tractable and posterior distribution.
result PDMP samplers can be improved to sample from multi-modal distributions.
New PDMP samplers tackle variable selection in models.
problem Jointly explore model space and parameter space.
method Develop reversible jump PDMP samplers.
result New samplers mix better and are more efficient.
Generative models using PDMPs with explicit jump rates and kernels.
problem Creating efficient generative models for complex data distributions.
method Piecewise deterministic Markov processes (PDMPs) with explicit expressions for jump rates and kernels.
result Efficient training and simulation methods for PDMP-based generative models.
PDMP samplers improve Bayesian PDE coefficient inference.
problem Efficient Bayesian inference in non-linear inverse problems with expensive likelihoods.
method Piecewise deterministic Markov process (PDMP) with surrogate-assisted thinning.
result PDMP samplers achieve higher accuracy and efficiency than traditional methods.
Modeling maximum drawdown records in capital markets using PDMP.
problem Capturing the statistical properties of maximum drawdown records in financial markets.
method Piecewise Deterministic Markov Process (PDMP) for modeling, statistical analysis of mean and variance, simulation study, parameter estimation techniques.
result Derivation of statistical results including mean and variance of maximum drawdown records.
New couplings improve understanding of molecular dynamics convergence.
problem Understanding convergence of Andersen dynamics in high dimensions.
method Presented couplings to obtain sharp convergence bounds in the Wasserstein sense.
result Sharp convergence bounds in the Wasserstein sense without global convexity.
New model predicts dynamic tax evasion with audits and imitation.
problem Static treatment of tax compliance and evasion in Bertotti and Modanese model.
method Piecewise Deterministic Markov Processes (PDMPs) for audits and imitation mechanisms.
result Model shows persistent fluctuations and stationary distribution, not extreme equilibrium.
New PDMP samplers improve BNN inference with accelerated computation.
problem Inference on Bayesian Neural Networks violates independence and posterior assumptions.
method Piecewise Deterministic Markov Process (PDMP) with adaptive thinning for inhomogenous Poisson Process (IPPs) sampling.
result PDMP samplers accelerate inference in BNNs, improving accuracy and mixing performance.
Optimal timing for converting savings into annuities considering mortality risk.
problem Determining the best time to annuitize retirement savings under stochastic mortality.
method Formulated as a three-dimensional optimal stopping problem, reduced to nested one-dimensional problems, solved using PDMP structure.
result Rich structure for the optimal annuitization rule, covering various parameter specifications.
Narendra-Shapiro (NS) algorithms are bandit-type algorithms that have been introduced in the sixties (with a view to applications in Psychology or learning automata), whose convergence has been intensively studied in the stochastic algorithm literature. In this paper, we adress the following question: are the Narendra-…
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a point process with stochastic intensity. We model the price impact as a linear fu…
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…
We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete n…
Study reveals convergence properties of SGD with random learning rate.
problem Analyzing convergence of SGD with random learning rate in non-convex optimization.
method Introduced Poisson SGD with random learning rate and used stationary distribution analysis.
result Poisson SGD converges to a stationary distribution and finds global minima in non-convex optimization.
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this context, one is interested in computing certain quantities of interest such as th…
Market makers optimize bid/ask quotes under hidden Markov chain uncertainty.
problem Optimizing market quotes with hidden factors affecting order intensities.
method Solves stochastic control problem using filtering, control, and PDMPs theory.
result Value function is unique viscosity solution of dynamic programming equation.