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101.
We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular. 相似文献
102.
Let F be a non-formally real field of characteristic not 2 and let W(F) be the Witt ring of F. In certain cases generators for the annihilator ideal are determined. Aim the primary decomposition of A(F) is given. For formally d fields F, as an analogue the primary decomposition of At(F) = {f(X) ∈ Z[X]| f(ω) = 0 for all ω ∈ Wt(F)}, where Wt(F) is the torsion part of the Witt group, is obtained. 相似文献
103.
Ai-guo Xiao Shou-fu Li Min Yang 《计算数学(英文版)》2001,19(3):269-280
1. IntroductionInvestigating whether a numerical method inherits some dynamical properties possessed bythe differential equation systems being integrated is an important field of numerical analysisand has received much attention in recent years See the review articlesof Sanz-Serna[9] and Section 11.16 of Hairer et. al.[2] for more detail concerning the symplectic methods. Most of the work on canonical iotegrators has dealt with one-step formulaesuch as Runge-Kutta methods and Runge'methods … 相似文献
104.
Jonathan Goodman 《Mathematical Programming》1985,33(2):162-171
We derive a quadratically convergent algorithm for minimizing a nonlinear function subject to nonlinear equality constraints. We show, following Kaufman [4], how to compute efficiently the derivative of a basis of the subspace tangent to the feasible surface. The derivation minimizes the use of Lagrange multipliers, producing multiplier estimates as a by-product of other calculations. An extension of Kantorovich's theorem shows that the algorithm maintains quadratic convergence even if the basis of the tangent space changes abruptly from iteration to iteration. The algorithm and its quadratic convergence are known but the drivation is new, simple, and suggests several new modifications of the algorithm. 相似文献
105.
In this paper we analyze conjugate gradient-type algorithms for solving convex quadratic programs subject only to box constraints (i.e., lower and upper bounds on the variables). Programs of this type, which we denote by BQP, play an important role in many optimization models and algorithms. We propose a new class of finite algorithms based on a nonfinite heuristic for solving a large, sparse BQP. The numerical results suggest that these algorithms are competitive with Dembo and Tulowitzski's (1983) CRGP algorithm in general, and perform better than CRGP for problems that have a low percentage of free variables at optimality, and for problems with only nonnegativity constraints. 相似文献
106.
This work reports a numerical study undertaken to investigate the dynamic response of a rotor supported by two turbulent flow
model journal bearings with nonlinear suspension and lubricated with couple stress fluid under quadratic damping. This may
be the first time that analysis of rotor-bearing system considered the quadratic damping effect. The dynamic response of the
rotor center and bearing center are studied. The analysis methods employed in this study are inclusive of the dynamic trajectories
of the rotor center and bearing center, power spectra, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent
analysis is also used to identify the onset of chaotic motion. The modeling results provide some useful insights into the
design and development of rotor-bearing system for rotating machinery that operates at highly rotational speed and highly
nonlinear regimes. 相似文献
107.
AMETHODPROVINGTHEUNIQUENESSOFTHELIMIT CYCLEOFTHEQUADRATICSYSTEMXuSilin(徐思林)(QingdaoUniversity,青岛大学,邮编:266071)ZhuYugen(朱豫根)(Na... 相似文献
108.
Hyunsuk Moon 《The Ramanujan Journal》2008,16(1):73-81
Let F(z)=∑
n=1∞
A(n)q
n
denote the unique weight 6 normalized cuspidal eigenform on Γ0(4). We prove that A(p)≡0,2,−1(mod 11) when p≠11 is a prime. We then use this congruence to give an application to the number of representations of an integer by quadratic
form of level 4.
相似文献
109.
We give a complete characterization of constant quadratic functions over an affine variety. This result is used to convexify
the objective function of a general quadratic programming problem (Pb) which contains linear equality constraints. Thanks
to this convexification, we show that one can express as a semidefinite program the dual of the partial Lagrangian relaxation
of (Pb) where the linear constraints are not relaxed. We apply these results by comparing two semidefinite relaxations made
from two sets of null quadratic functions over an affine variety.
相似文献
110.
By means of the theory of modular forms the formulas for a number of representations of positive integers by two positive quaternary quadratic forms of steps 36 and 60 and by all positive diagonal quadratic forms with seven variables of step 8 are obtain. 相似文献