We introduce an approach for valuing some path-dependent options in a discrete-time Markov chain market based on the characteristic function of a vector of occupation times of the chain. A pricing kernel is introduced...
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We introduce an approach for valuing some path-dependent options in a discrete-time Markov chain market based on the characteristic function of a vector of occupation times of the chain. A pricing kernel is introduced and analytical formulas for the prices of Asian options and occupation time call options are derived. (C) 2011 Elsevier Ltd. All rights reserved.
The material here is motivated by the discussion of solutions of linear homogeneous and autonomous differential equations with deviating arguments. If a, b, c and {(sic)(l)} are real and gamma((sic)) is real-valued an...
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The material here is motivated by the discussion of solutions of linear homogeneous and autonomous differential equations with deviating arguments. If a, b, c and {(sic)(l)} are real and gamma((sic)) is real-valued and continuous, an example with these parameters is u'(t) = {au(t) + bu(t + (sic)(1)) + cu(t + (sic)(2))} + integral((sic)4)((sic)3) gamma((sic))(s)u(t+s)ds. (star) A wide class of equations (star), or of similar type, can be written in the "canonical" form u'(t) = integral(tau max)(tau min) u(t+s)d sigma(s) (t is an element of R), for a suitable choice of tau(min), tau(max) (star star) where sigma is of bounded variation and the integral is a Riemann-Stieltjes integral. For equations written in the form (star star), there is a corresponding characteristic function chi(zeta)) := zeta-integral(tau max)(tau min) exp(zeta s)d sigma(s) (zeta is an element of C), (star star star) whose zeros (if one considers appropriate subsets of equations (star star) - the literature provides additional information on the subsets to which we refer) play a role in the study of oscillatory or non-oscillatory solutions, or of bounded or unbounded solutions. We show that the related discussion of the zeros of chi is facilitated by observing and exploiting some simple and fundamental properties of characteristic functions. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from thedata. However, if the process is non-Gaussian, PCA algorithms or their higher order gener...
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Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from thedata. However, if the process is non-Gaussian, PCA algorithms or their higher order generalizations provide only incomplete or misleading information on the statistical properties of the data. To handle such situations we propose neural network algorithms, with an hybrid (supervised and unsupervised) learning scheme, which constructs the characteristic function of the probability distribution and the transition functions of the stochastic process. Illustrative examples are presented, which include Cauchy and Levy-type processes. (C) 1997 Elsevier Science Ltd.
We propose necessary and sufficient conditions for a complex-valued function f on to be a characteristic function of a probability measure. Certain analytic extensions of f to tubular domains in are studied. In order ...
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We propose necessary and sufficient conditions for a complex-valued function f on to be a characteristic function of a probability measure. Certain analytic extensions of f to tubular domains in are studied. In order to extend the class of functions under study, we also consider the case where f is a generalized function (distribution). The main result is given in terms of completely monotonic functions on convex cones in R-n.
It is shown that there exists a one-to-one correspondence between the direct and inverse Weyl transform approach, on the one side, and the (symplectic) tomographic representation of quantum mechanics, on the other sid...
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It is shown that there exists a one-to-one correspondence between the direct and inverse Weyl transform approach, on the one side, and the (symplectic) tomographic representation of quantum mechanics, on the other side. In view of this correspondence, the star-product quantization based on characteristic functions is introduced.
Let Omega be a set and Omega(1),..., Omega(m-1) subsets of Omega, being m an integer greater than one. For a given function f = (f(1) ,... f(m)) : Omega -> R-m, we prove the existence of a unique function alpha = (...
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Let Omega be a set and Omega(1),..., Omega(m-1) subsets of Omega, being m an integer greater than one. For a given function f = (f(1) ,... f(m)) : Omega -> R-m, we prove the existence of a unique function alpha = (alpha(1),..., alpha(m)) : Omega -> R-m such that {alpha(i) = alpha(i+1) on Omega(i ) alpha(1) + ... + alpha(i) = f(1) + ... + f(i) on Omega \ Omega(i), for all i < m alpha(1) + ... + alpha(m) = f(1) + ... + f(m), called the average function of f : Omega -> R-m relatively to (Omega, Omega(1 ),..., Omega(m-1)). When Omega is a topological space and f is a continuous function, we find necessary and sufficient conditions for the continuity of the average function of f. We write alpha(i) as a linear combination of characteristic functions of the (coincidence) sets boolean AND(s)(j=r) Omega(j), 1 <= r <= s <= m - 1, belonging the coefficients to Q[f(1) ,..., f(m)].
A new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented. The system is expressed by a set of time-varying discrete systems with non-Gaussian stochastic input and nonlinea...
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A new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented. The system is expressed by a set of time-varying discrete systems with non-Gaussian stochastic input and nonlinear output. A new concept, such as hybrid characteristic function, is introduced to describe the stochastic nature of the dynamic conditional estimation errors, where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution. For this purpose, the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs, and the properties of the hybrid characteristic function, are established. A new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error. An analytical solution, which guarantees the filter gain matrix to be an optimal one, is then obtained. A simulation case study is included to show the effectiveness of the proposed algorithm, and encouraging results have been obtained. (C) 2009 Elsevier Ltd. All rights reserved.
Let j(mm) = ((Im)(0) - (0)(Im)), J(m) = ((0)(iIm) - (-iIm)(0)), I-m is the identity matrix of order m. Let W(lambda) be an entire matrix valued function of order 2m, W(0) = I-2m, the values of W(lambda) are j(mm)-unit...
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Let j(mm) = ((Im)(0) - (0)(Im)), J(m) = ((0)(iIm) - (-iIm)(0)), I-m is the identity matrix of order m. Let W(lambda) be an entire matrix valued function of order 2m, W(0) = I-2m, the values of W(lambda) are j(mm)-unitary at the imaginary axis and strictly j(mm)-expansive in the open right half-plane. The blocks of order m of the matrix W(lambda) with appropriate signs are treated as coefficients of algebraic Riccati equation. It is proved that for any lambda with positive real part this equation has a unique contractive solution theta(lambda). The matrix valued function theta (lambda) can be represented in a form theta (lambda) = theta(A) (i lambda) where theta(A)(mu) is the characteristic function of some maximal dissipative operator A. This operator is in a natural way constructed starting from the Hamiltonian system of the form dx (tau)/d tau = iJ(m)K(tau)x(tau), tau is an element of [0;+infinity) with periodic coefficients.
A unifying and generalizing approach to representations of the positive-part and absolute moments and of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related repres...
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A unifying and generalizing approach to representations of the positive-part and absolute moments and of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related representations of the c.f. of , generalized moments , truncated moments, and the distribution function, is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed.
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