3,406 research outputs found
Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes
Fast pricing of American-style options has been a difficult problem since it
was first introduced to financial markets in 1970s, especially when the
underlying stocks' prices follow some jump-diffusion processes. In this paper,
we propose a new algorithm to generate tight upper bounds on the Bermudan
option price without nested simulation, under the jump-diffusion setting. By
exploiting the martingale representation theorem for jump processes on the dual
martingale, we are able to explore the unique structure of the optimal dual
martingale and construct an approximation that preserves the martingale
property. The resulting upper bound estimator avoids the nested Monte Carlo
simulation suffered by the original primal-dual algorithm, therefore
significantly improves the computational efficiency. Theoretical analysis is
provided to guarantee the quality of the martingale approximation. Numerical
experiments are conducted to verify the efficiency of our proposed algorithm
Multi-Valued Verification of Strategic Ability
Some multi-agent scenarios call for the possibility of evaluating
specifications in a richer domain of truth values. Examples include runtime
monitoring of a temporal property over a growing prefix of an infinite path,
inconsistency analysis in distributed databases, and verification methods that
use incomplete anytime algorithms, such as bounded model checking. In this
paper, we present multi-valued alternating-time temporal logic (mv-ATL*), an
expressive logic to specify strategic abilities in multi-agent systems. It is
well known that, for branching-time logics, a general method for
model-independent translation from multi-valued to two-valued model checking
exists. We show that the method cannot be directly extended to mv-ATL*. We also
propose two ways of overcoming the problem. Firstly, we identify constraints on
formulas for which the model-independent translation can be suitably adapted.
Secondly, we present a model-dependent reduction that can be applied to all
formulas of mv-ATL*. We show that, in all cases, the complexity of verification
increases only linearly when new truth values are added to the evaluation
domain. We also consider several examples that show possible applications of
mv-ATL* and motivate its use for model checking multi-agent systems
High order filtering methods for approximating hyberbolic systems of conservation laws
In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method
On the Expressiveness and Complexity of ATL
ATL is a temporal logic geared towards the specification and verification of
properties in multi-agents systems. It allows to reason on the existence of
strategies for coalitions of agents in order to enforce a given property. In
this paper, we first precisely characterize the complexity of ATL
model-checking over Alternating Transition Systems and Concurrent Game
Structures when the number of agents is not fixed. We prove that it is
\Delta^P_2 - and \Delta^P_?_3-complete, depending on the underlying multi-agent
model (ATS and CGS resp.). We also consider the same problems for some
extensions of ATL. We then consider expressiveness issues. We show how ATS and
CGS are related and provide translations between these models w.r.t.
alternating bisimulation. We also prove that the standard definition of ATL
(built on modalities "Next", "Always" and "Until") cannot express the duals of
its modalities: it is necessary to explicitely add the modality "Release".Comment: 25 page
An enhanced concave program relaxation for choice network revenue management
The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm
when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ESDCPκ, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the
benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC
runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small
Regularization and Model Selection with Categorial Predictors and Effect Modifiers in Generalized Linear Models
We consider varying-coefficient models with categorial effect modifiers in the framework of generalized linear models. We distinguish between nominal and ordinal effect modifiers, and propose adequate Lasso-type regularization techniques that allow for (1) selection of relevant covariates, and (2) identification of coefficient functions that are actually varying with the level of a potentially effect modifying factor. We investigate the estimators’ large sample properties, and show in simulation studies that the proposed approaches perform very well for finite samples, too. Furthermore, the presented methods are compared with alternative procedures, and applied to real-world medical data
PhysicsGP: A Genetic Programming Approach to Event Selection
We present a novel multivariate classification technique based on Genetic
Programming. The technique is distinct from Genetic Algorithms and offers
several advantages compared to Neural Networks and Support Vector Machines. The
technique optimizes a set of human-readable classifiers with respect to some
user-defined performance measure. We calculate the Vapnik-Chervonenkis
dimension of this class of learning machines and consider a practical example:
the search for the Standard Model Higgs Boson at the LHC. The resulting
classifier is very fast to evaluate, human-readable, and easily portable. The
software may be downloaded at: http://cern.ch/~cranmer/PhysicsGP.htmlComment: 16 pages 9 figures, 1 table. Submitted to Comput. Phys. Commu
An enhanced concave program relaxation for choice network revenue management
The network choice revenue management problem models customers as choosing from an offer-set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the ?SDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.discrete-choice models, network revenue management, optimization
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