21,678 research outputs found
On Feedback Control in Kelly Betting: An Approximation Approach
In this paper, we consider a simple discrete-time optimal betting problem
using the celebrated Kelly criterion, which calls for maximization of the
expected logarithmic growth of wealth. While the classical Kelly betting
problem can be solved via standard concave programming technique, an
alternative but attractive approach is to invoke a Taylor-based approximation,
which recasts the problem into quadratic programming and obtain the closed-form
approximate solution. The focal point of this paper is to fill some voids in
the existing results by providing some interesting properties when such an
approximate solution is used. Specifically, the best achievable betting
performance, positivity of expected cumulative gain or loss and its associated
variance, expected growth property, variance of logarithmic growth, and results
related to the so-called survivability (no bankruptcy) are provided.Comment: To appear in the proceedings of the 2020 IEEE Conference on Control
Technology and Applications (CCTA
Tunable Fano-Kondo resonance in side-coupled double quantum dot system
We study the interference between the Fano and Kondo effects in a
side-coupled double-quantum- dot system where one of the quantum dots couples
to conduction electron bath while the other dot only side-couples to the first
dot via antiferromagnetic (AF) spin exchange coupling. We apply both the
perturbative renormalization group (RG) and numerical renormalization group
(NRG) approaches to study the effect of AF coupling on the Fano lineshape in
the conduction leads. With particle-hole symmetry, the AF exchange coupling
competes with the Kondo effect and leads to a local spin-singlet ground state
for arbitrary small coupling, so called "two-stage Kondo effect". As a result,
via NRG we find the spectral properties of the Fano lineshape in the tunneling
density of states (TDOS) of conduction electron leads shows double dip-peak
features at the energy scale around the Kondo temperature and the one much
below it, corresponding to the two-stage Kondo effect; it also shows an
universal scaling behavior at very low energies. We find the qualitative
agreement between the NRG and the perturbative RG approach. Relevance of our
work to the experiments is discussed.Comment: 7 pages, 7 figure
Properties of Microlensing Central Perturbations by Planets in Binary Stellar Systems under the Strong Finite-Source Effect
We investigate high-magnification events caused by planets in wide binary
stellar systems under the strong finite-source effect, where the planet orbits
one of the companions. From this, we find that the pattern of central
perturbations in triple lens systems commonly appears as a combination of
individual characteristic patterns of planetary and binary lens systems in a
certain range where the sizes of the caustics induced by a planet and a binary
companion are comparable, and the range changes with the mass ratio of the
planet to the planet-hosting star. Specially, we find that because of this
central perturbation pattern, the characteristic feature of high-magnification
events caused by the triple lens systems appears in the residual from the
single-lensing light curve despite the strong finite-source effect, and it is
discriminated from those of the planetary and binary lensing events and thus
can be used for the identification of the existence of both planet and binary
companion. This characteristic feature is a simultaneous appearance of two
features. First, double negative-spike and single positive-spike features
caused by the binary companion appear together in the residual, where the
double negative spike occurs at both moments when the source enters and exits
the caustic center and the single positive spike occurs at the moment just
before the source enters into or just after the source exits from the caustic
center. Second, the magnification excess before or after the single
positive-spike feature is positive due to the planet, and the positive excess
has a remarkable increasing or decreasing pattern depending on the source
trajectory.Comment: 12 pages, 3 figures, accepted for publication in Ap
On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important
The focal point of this paper is the issue of "drawdown" which arises in
recursive betting scenarios and related applications in the stock market.
Roughly speaking, drawdown is understood to mean drops in wealth over time from
peaks to subsequent lows. Motivated by the fact that this issue is of paramount
concern to conservative investors, we dispense with the classical variance as
the risk metric and work with drawdown and mean return as the risk-reward pair.
In this setting, the main results in this paper address the so-called
"efficiency" of linear time-invariant (LTI) investment feedback strategies
which correspond to Markowitz-style schemes in the finance literature. Our
analysis begins with the following principle which is widely used in finance:
Given two investment opportunities, if one of them has higher risk and lower
return, it will be deemed to be inefficient or strictly dominated and generally
rejected in the marketplace. In this framework, with risk-reward pair as
described above, our main result is that classical Markowitz-style strategies
are inefficient. To establish this, we use a new investment strategy which
involves a time-varying linear feedback block K(k), called the drawdown
modulator. Using this instead of the original LTI feedback block K in the
Markowitz scheme, the desired domination is obtained. As a bonus, it is also
seen that the modulator assures a worst-case level of drawdown protection with
probability one.Comment: This paper has been published in Proceedings of 56th IEEE Conference
on Decision and Control (CDC) 201
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