83,051 research outputs found
A Distributed Tracking Algorithm for Reconstruction of Graph Signals
The rapid development of signal processing on graphs provides a new
perspective for processing large-scale data associated with irregular domains.
In many practical applications, it is necessary to handle massive data sets
through complex networks, in which most nodes have limited computing power.
Designing efficient distributed algorithms is critical for this task. This
paper focuses on the distributed reconstruction of a time-varying bandlimited
graph signal based on observations sampled at a subset of selected nodes. A
distributed least square reconstruction (DLSR) algorithm is proposed to recover
the unknown signal iteratively, by allowing neighboring nodes to communicate
with one another and make fast updates. DLSR uses a decay scheme to annihilate
the out-of-band energy occurring in the reconstruction process, which is
inevitably caused by the transmission delay in distributed systems. Proof of
convergence and error bounds for DLSR are provided in this paper, suggesting
that the algorithm is able to track time-varying graph signals and perfectly
reconstruct time-invariant signals. The DLSR algorithm is numerically
experimented with synthetic data and real-world sensor network data, which
verifies its ability in tracking slowly time-varying graph signals.Comment: 30 pages, 9 figures, 2 tables, journal pape
Quantile Hedging in a Semi-Static Market with Model Uncertainty
With model uncertainty characterized by a convex, possibly non-dominated set
of probability measures, the agent minimizes the cost of hedging a path
dependent contingent claim with given expected success ratio, in a
discrete-time, semi-static market of stocks and options. Based on duality
results which link quantile hedging to a randomized composite hypothesis test,
an arbitrage-free discretization of the market is proposed as an approximation.
The discretized market has a dominating measure, which guarantees the existence
of the optimal hedging strategy and helps numerical calculation of the quantile
hedging price. As the discretization becomes finer, the approximate quantile
hedging price converges and the hedging strategy is asymptotically optimal in
the original market.Comment: Final version. To appear in the Mathematical Methods of Operations
Research. Keywords: Quantile hedging, expected success ratio, model
uncertainty, semi-static hedging, Neyman-Pearson Lemm
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