10,849 research outputs found
Convexity of ruin probability and optimal dividend strategies for a general Levy process
In this paper, we consider the optimal dividends problem for a company whose
cash reserves follow a general Levy process with certain positive jumps and
arbitrary negative jumps. The objective is to find a policy which maximizes the
expected discounted dividends until the time of ruin. Under appropriate
conditions, we appeal to very recent results in the theory of potential
analysis of subordinators to obtain the convexity properties of probability of
ruin. We present conditions under which the optimal dividend strategy, among
all admissible ones, takes the form of a barrier strategy.Comment: 19 pages, corrected some typo
Reconstructing propagation networks with natural diversity and identifying hidden sources
Our ability to uncover complex network structure and dynamics from data is
fundamental to understanding and controlling collective dynamics in complex
systems. Despite recent progress in this area, reconstructing networks with
stochastic dynamical processes from limited time series remains to be an
outstanding problem. Here we develop a framework based on compressed sensing to
reconstruct complex networks on which stochastic spreading dynamics take place.
We apply the methodology to a large number of model and real networks, finding
that a full reconstruction of inhomogeneous interactions can be achieved from
small amounts of polarized (binary) data, a virtue of compressed sensing.
Further, we demonstrate that a hidden source that triggers the spreading
process but is externally inaccessible can be ascertained and located with high
confidence in the absence of direct routes of propagation from it. Our approach
thus establishes a paradigm for tracing and controlling epidemic invasion and
information diffusion in complex networked systems.Comment: 20 pages and 5 figures. For Supplementary information, please see
http://www.nature.com/ncomms/2014/140711/ncomms5323/full/ncomms5323.html#
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