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We provide closed-form solutions for European option values when the dynamics of both the short rate and volatility of the underlying price process are modulated by a continuous-time Markov chain with a finite number of “economic states”. Extensions involving dividends, currencies and cost of carry are further explored. 相似文献
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Abdulla Al Mamon Kazuharu Bamba 《The European Physical Journal C - Particles and Fields》2018,78(10):862
We study the accelerated expansion phase of the universe by using the kinematic approach. In particular, the deceleration parameter q is parametrized in a model-independent way. Considering a generalized parametrization for q, we first obtain the jerk parameter j (a dimensionless third time derivative of the scale factor) and then confront it with cosmic observations. We use the latest observational dataset of the Hubble parameter H(z) consisting of 41 data points in the redshift range of \(0.07 \le z \le 2.36\), larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter \(q_0\), jerk parameter \(j_0\) and transition redshift \(z_t\) (at which the expansion of the universe switches from being decelerated to accelerated) with \(1\sigma \) errors (\(68.3\%\) confidence level). As a result, it is demonstrate that the universe is indeed undergoing an accelerated expansion phase following the decelerated one. This is consistent with the present observations. Moreover, we find the departure for the present model from the standard \(\Lambda \)CDM model according to the evolution of j. Furthermore, the evolution of the normalized Hubble parameter is shown for the present model and it is compared with the dataset of H(z). 相似文献
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Fuqi Chen Rogemar Mamon Sévérien Nkurunziza 《Annals of the Institute of Statistical Mathematics》2018,70(4):807-853
Determining accurately when regime and structural changes occur in various time-series data is critical in many social and natural sciences. We develop and show further the equivalence of two consistent estimation techniques in locating the change point under the framework of a generalised version of the one-dimensional Ornstein–Uhlenbeck process. Our methods are based on the least sum of squared error and the maximum log-likelihood approaches. The case where both the existence and the location of the change point are unknown is investigated and an informational methodology is employed to address these issues. Numerical illustrations are presented to assess the methods’ performance. 相似文献
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Three Ways to Solve for Bond Prices in the Vasicek Model 总被引:3,自引:0,他引:3
Three approaches in obtaining the closed-form solution of the Vasicek bond pricing problem are discussed in this exposition. A derivation based solely on the distribution of the short rate process is reviewed. Solving the bond price partial differential equation (PDE) is another method. In this paper, this PDE is derived via a martingale approach and the bond price is determined by integrating ordinary differential equations. The bond pricing problem is further considered within the Heath-Jarrow-Morton (HJM) framework in which the analytic solution follows directly from the short rate dynamics under the forward measure. 相似文献
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Mamon Dey Nayanmoni Gogoi 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2013,125(49):13014-13016
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Mamon Dey Dr. Nayanmoni Gogoi 《Angewandte Chemie (International ed. in English)》2013,52(49):12780-12782
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Mathematical Notes - 相似文献
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A new algorithm is proposed for generating scenarios from a partially specified symmetric multivariate distribution. The algorithm generates samples which match the first two moments exactly, and match the marginal fourth moments approximately, using a semidefinite programming procedure. The performance of the algorithm is illustrated by a numerical example. 相似文献
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