Deriving option prices from operational-time Markov lattices
problem Option pricing
method Operational-time Markov lattice
result Derives option-pricing equations from an operational-time Markov lattice
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15 results for “operational-time”
Derives operational-time variance kernel for reaction boundaries in financial markets.
problem Separating components in volatility models to better understand market dynamics.
method Derives a variance kernel for a latent-order-book reaction boundary, separating structural boundary cumulant, clock projection, and pricing-measure choice.
result Operational variance has a closed asymptotic form for long-memory forcing, with effective signed-forcing intensity and resilience.
In this study we model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the p…
Derives variance kernel for reaction boundary in financial models.
problem Separating components in financial volatility models.
method Operational-time variance kernel, damped Abel response kernel, closed asymptotic form.
result Operational variance has a closed asymptotic form involving various parameters.
The paper challenges the assumption of a unique global time in financial markets, highlighting market incompleteness.
problem The assumption of a unique global time in financial markets is challenged.
method The paper contrasts event-time, renewal, point-process, and order-flow descriptions of financial markets.
result Non-uniqueness of time leads to a more foundational form of market incompleteness.
Designs adaptive controller for networked control systems with wireless data transmission.
problem Adaptive control in networked systems with unreliable wireless channels.
method Upper Confidence Bounds for Networked Control Systems (UCB-NCS) learning rule.
result Non-asymptotic performance guarantees with a regret bound of O(C√T).
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
Quantum hybrid vision transformers improve event classification in high energy physics.
problem Excessive computational resources for training and deploying vision transformer models.
method Constructed quantum hybrid vision transformers for high energy physics event classification.
result Quantum hybrid models achieve comparable performance to classical models with fewer parameters.
Within the context of risk integration, we introduce in risk measurement stochastic holding period (SHP) models. This is done in order to obtain a `liquidity-adjusted risk measure' characterized by the absence of a fixed time horizon. The underlying assumption is that - due to changes on market liquidity conditions - o…
SKOLR uses linear RNNs to approximate Koopman operators for time-series forecasting.
problem Nonlinear dynamical system analysis and time-series forecasting with infinite-dimensional Koopman operators.
method Established a connection between Koopman operator approximation and linear RNNs, integrating learnable spectral decomposition and MLP.
result SKOLR delivers exceptional performance in various forecasting benchmarks and dynamical systems.
Remaining Useful Life (RUL) of an equipment or one of its components is defined as the time left until the equipment or component reaches its end of useful life. Accurate RUL estimation is exceptionally beneficial to Predictive Maintenance, and Prognostics and Health Management (PHM). Data driven approaches which lever…
Balanced Neural ODEs combine VAEs and Neural ODEs for efficient time series modeling.
problem Efficiently modeling systems with time-varying inputs and varying complexity.
method Combines VAEs for dimensionality reduction and Neural ODEs for dynamics, using variational parameters to adaptively learn.
result Balanced Neural ODEs (B-NODE) efficiently approximate Koopman operator without predefined dimensionality.
Revisiting Trade-sign Long-memory and Square-root Law price impact
problem Revisiting the Lillo-Mike-Farmer (LMF) theory and the square-root law (SQRL) of meta-order impact
method Using a coupled discrete reaction-diffusion formulation
result Long-memory of trade signs and square-root law of meta-order impact
Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.
problem Challenges in time-dependent reliability analysis of nonlinear dynamical systems.
method Koopman operator approach for transforming nonlinear systems into linear ones, combined with deep learning for intrinsic coordinates.
result Robust and generalizable approach for time-dependent reliability analysis, superior to purely data-driven methods.
A digital twin for multi-scale systems uses physics-based and machine learning models.
problem Lack of application-specific details in digital twin technology.
method Strategically separates into physics-based and data-driven models; uses mixture of experts with Gaussian Process.
result Robust and accurate predictions at future time-steps for multi-scale systems.