800 research outputs found
Optimal control of the state statistics for a linear stochastic system
We consider a variant of the classical linear quadratic Gaussian regulator
(LQG) in which penalties on the endpoint state are replaced by the
specification of the terminal state distribution. The resulting theory
considerably differs from LQG as well as from formulations that bound the
probability of violating state constraints. We develop results for optimal
state-feedback control in the two cases where i) steering of the state
distribution is to take place over a finite window of time with minimum energy,
and ii) the goal is to maintain the state at a stationary distribution over an
infinite horizon with minimum power. For both problems the distribution of
noise and state are Gaussian. In the first case, we show that provided the
system is controllable, the state can be steered to any terminal Gaussian
distribution over any specified finite time-interval. In the second case, we
characterize explicitly the covariance of admissible stationary state
distributions that can be maintained with constant state-feedback control. The
conditions for optimality are expressed in terms of a system of dynamically
coupled Riccati equations in the finite horizon case and in terms of algebraic
conditions for the stationary case. In the case where the noise and control
share identical input channels, the Riccati equations for finite-horizon
steering become homogeneous and can be solved in closed form. The present paper
is largely based on our recent work in arxiv.org/abs/1408.2222,
arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1410.344
Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction
In this paper we develop a novel neural network model for predicting implied
volatility surface. Prior financial domain knowledge is taken into account. A
new activation function that incorporates volatility smile is proposed, which
is used for the hidden nodes that process the underlying asset price. In
addition, financial conditions, such as the absence of arbitrage, the
boundaries and the asymptotic slope, are embedded into the loss function. This
is one of the very first studies which discuss a methodological framework that
incorporates prior financial domain knowledge into neural network architecture
design and model training. The proposed model outperforms the benchmarked
models with the option data on the S&P 500 index over 20 years. More
importantly, the domain knowledge is satisfied empirically, showing the model
is consistent with the existing financial theories and conditions related to
implied volatility surface.Comment: 8 pages, SIGKDD 202
Whom to Ask? Jury Selection for Decision Making Tasks on Micro-blog Services
It is universal to see people obtain knowledge on micro-blog services by
asking others decision making questions. In this paper, we study the Jury
Selection Problem(JSP) by utilizing crowdsourcing for decision making tasks on
micro-blog services. Specifically, the problem is to enroll a subset of crowd
under a limited budget, whose aggregated wisdom via Majority Voting scheme has
the lowest probability of drawing a wrong answer(Jury Error Rate-JER). Due to
various individual error-rates of the crowd, the calculation of JER is
non-trivial. Firstly, we explicitly state that JER is the probability when the
number of wrong jurors is larger than half of the size of a jury. To avoid the
exponentially increasing calculation of JER, we propose two efficient
algorithms and an effective bounding technique. Furthermore, we study the Jury
Selection Problem on two crowdsourcing models, one is for altruistic
users(AltrM) and the other is for incentive-requiring users(PayM) who require
extra payment when enrolled into a task. For the AltrM model, we prove the
monotonicity of JER on individual error rate and propose an efficient exact
algorithm for JSP. For the PayM model, we prove the NP-hardness of JSP on PayM
and propose an efficient greedy-based heuristic algorithm. Finally, we conduct
a series of experiments to investigate the traits of JSP, and validate the
efficiency and effectiveness of our proposed algorithms on both synthetic and
real micro-blog data.Comment: VLDB201
On the Relation Between Optimal Transport and Schr\uf6dinger Bridges: A Stochastic Control Viewpoint
We take a new look at the relation between the optimal transport problem
and the Schr\uf6dinger bridge problem from a stochastic control perspective. Our aim is
to highlight new connections between the two that are richer and deeper than those
previously described in the literature. We begin with an elementary derivation of
the Benamou\u2013Brenier fluid dynamic version of the optimal transport problem and
provide, in parallel, a new fluid dynamic version of the Schr\uf6dinger bridge problem.
We observe that the latter establishes an important connection with optimal transport
without zero-noise limits and solves a question posed by Eric Carlen in 2006. Indeed,
the two variational problems differ by a Fisher information functional. We motivate
and consider a generalization of optimal mass transport in the form of a (fluid dynamic)
problem of optimal transport with prior. This can be seen as the zero-noise limit of
Schr\uf6dinger bridges when the prior is any Markovian evolution.We finally specialize
to the Gaussian case and derive an explicit computational theory based on matrix
Riccati differential equations. A numerical example involving Brownian particles is
also provided
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