One of the most important problems in option pricing theory is the valuation and optimal exercise of derivatives with American-style exercise features. These types of derivatives are found in all major financial marke...
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One of the most important problems in option pricing theory is the valuation and optimal exercise of derivatives with American-style exercise features. These types of derivatives are found in all major financial markets. Simulation is a promising alternative to traditional numerical methods and has many advantages as a framework for valuing American options. Recently, Longstaff and Schwartz presented a simple, yet powerful, least-squares Monte Carlo (LSM) algorithm to approximating the value of US options by simulation. This article provides computational complexity analysis of the LSM algorithm. Essentially, the technique of computational complexity analysis is to break down a computational algorithm into logical modules and analyze the effect on the algorithm of adding or deleting logical modules. computational complexity analysis is important in algorithm design because of structural differences in computer and human logic. Algorithms that seem perfectly natural and logical from the human perspective may sometime be found to contain unnecessary complexity when analysed from the computer's perspective. The results showed that a new algorithm constructed by removing the least-squares module altogether from the LSM algorithm improves not only the computational speed, but also produces results that are more accurate than the LSM.
We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a green algebra generated by a set of pairs, and determi...
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ISBN:
(纸本)0769507255
We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a green algebra generated by a set of pairs, and determining, whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a gir en algebra containing a gh en set of pairs. We prole that this problem is complete for nondeterministic polynomial time.
Within the framework of membrane systems, distributed parallel computing models inspired by the functioning of the living cell, various computational complexity classes have been defined, which can be compared against...
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ISBN:
(纸本)9783642139611
Within the framework of membrane systems, distributed parallel computing models inspired by the functioning of the living cell, various computational complexity classes have been defined, which can be compared against the computational complexity classes defined for Turing machines. Here some issues and results concerning computational complexity of membrane systems are discussed. In particular, we focus our attention on the comparison among complexity classes for membrane systems with active membranes (where new membranes can be created by division of membranes which exist in the system in a given moment) and the classes PSPACE, EXP, and EXPSPACE.
The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete e...
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ISBN:
(纸本)9783030865931;9783030865924
The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under supervisory control. Here, we study the computational complexity of this problem for the class of sparse regular constraint languages. We give a new characterization of sparse regular sets, which equal the bounded regular sets, and derive a full classification of the computational complexity of CSP for letter-bounded regular constraint languages, which properly contain the strictly bounded regular languages. Then, we introduce strongly self-synchronizing codes and investigate CSP for bounded languages induced by these codes. With our previous result, we deduce a full classification for these languages as well. In both cases, depending on the constraint language, our problem becomes N P-complete or polynomial time solvable.
We study the computational complexity of proper equilibrium in finite games and prove the following results. First, for two-player games in strategic form we show that the task of simply verifying the proper equilibri...
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ISBN:
(纸本)9781450358293
We study the computational complexity of proper equilibrium in finite games and prove the following results. First, for two-player games in strategic form we show that the task of simply verifying the proper equilibrium conditions of a given pure Nash equilibrium is NP-complete. Next, for n-player games in strategic form we show that the task of computing an approximation of a proper equilibrium is FIXPa-complete. Finally, for n-player polymatrix games we show that the task of computing a symbolic proper equilibrium is PPAD-complete.
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great...
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ISBN:
(纸本)9781457719219
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of their low multiplicative and overall complexities. However, their advantages are shown by inspection in the literature, and there is no asymptotic computational complexity analysis for CFFTs. Their high additive complexity also incurs difficulties in hardware implementations. In this paper, we derive the bounds for the multiplicative and additive complexities of CFFTs, respectively. Our results confirm that CFFTs have the smallest multiplicative complexities among all known algorithms while their additive complexities render them asymptotically suboptimal. However, CFFTs remain valuable as they have the smallest overall complexities for most practical lengths. Our additive complexity analysis also leads to a structured addition network, which not only has low complexity but also is suitable for hardware implementations.
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint lang...
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ISBN:
(纸本)9783030581503;9783030581497
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constrained synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, N P-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constrained synchronization problem, given a constraint automaton accepting a commutative language as input.
We analyze the computational complexity of various two-dimensional platform games. We state and prove several meta-theorems that identify a class of these games for which the set of solvable levels is NP-hard, and ano...
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ISBN:
(纸本)9783642131219
We analyze the computational complexity of various two-dimensional platform games. We state and prove several meta-theorems that identify a class of these games for which the set of solvable levels is NP-hard, and another class for which the set is even PSPACE-hard. Notably COMMANDERKEEN is shown to be NP-hard, and PRINCEOFPERSIA is shown to be PSPACE-complete. We then analyze the related game Lemmings, where we construct a set of instances which only have exponentially long solutions. This shows that an assumption by Cormode in [3] is false and invalidates the proof that the general version of the LEMMINGS decision problem is in NP. We then augment our construction to only include one entrance, which makes our instances perfectly natural within the context of the original game.
The paper gives the computational complexity of the robust Schur stability analysis by the generalized stability feeler. computational complexity of robust stability analysis is considered as an important characterist...
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ISBN:
(纸本)9781922107398
The paper gives the computational complexity of the robust Schur stability analysis by the generalized stability feeler. computational complexity of robust stability analysis is considered as an important characteristic to evaluate robust stability analysis methods. We derive the computational complexity from the algorithm of the generalized stability feeler. The result shows that the robust Schur stability can be checked in polynomial time.
Bertsekas recently proposed Asynchronous Policy Iteration (API) as an alternative algorithm of Policy Iteration (PI) for solving the problem of two-player zero-sum Markov games. To quantifying the benefits of API, bes...
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ISBN:
(纸本)9798350344868;9798350344851
Bertsekas recently proposed Asynchronous Policy Iteration (API) as an alternative algorithm of Policy Iteration (PI) for solving the problem of two-player zero-sum Markov games. To quantifying the benefits of API, besides its flexibility for parallel and asynchronous implementation, the focus of this paper is to derive the computational complexity of API. We show that to reach within. error to the optimal value function, the computational complexity of API is at most O (poly (n, m(1), m(2), ln(1/(1 -gamma))), where n is the number of states, m(1), m(2) are the number of actions for player 1 and player 2 respectively, and gamma is the discount factor.
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