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- Wu, Shiquan 7 (%)
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## Pricing and hedging of American contingent claims in incomplete markets

### Acta Mathematicae Applicatae Sinica (1999-04-01) 15: 144-152 , April 01, 1999

This paper studies the pricing and hedging for American contingent claims in an incomplete market under mild conditions using the numeraire method to avoid changes of probability measure. When the market is incomplete, prices can not be derived by no-arbitrage arguments, since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolio of the basic securities. We adopt the method of fictitious completion of [1] to provide an upper bound and a lower bound for the actual market price of the claim.

## A dual non-linear program

### Acta Mathematicae Applicatae Sinica (1984-09-01) 1: 163-167 , September 01, 1984

In the paper a dual of a nonlinear fractional functional programming problem has been formulated. This problem can be used to obtain a solution of the mixed 0–1 integer linear programming problem. Some properties related to the primal and dual have been given.

## On the spectral properties ofM-matrices and its applications

### Acta Mathematicae Applicatae Sinica (1999-10-01) 15: 418-424 , October 01, 1999

Let*A* be an*M*-matrix and*B* be a*Z*-matrix. In this paper we reveal the spectral relationship of*A* and*B* under some interesting conditions. Applying this result, we solve an open problem on splittings of an*M*-matrix and partially answer an open problem on the level diagrams for*A* and*B*.

## On Nonexistence of Algebraic Curve Solutions to Second-order Polynomial Autonomous Systems Over the Complex Field

### Acta Mathematicae Applicatae Sinica (2002-11-01) 18: 657-662 , November 01, 2002

###
*Abstract*

In this paper, by using the method of algebraic analysis, the results in our previous work are generalized. These results are of importance in the qualitative theory of polynomial autonomous systems.

## Ruin Probabilities under a Markovian Risk Model

### Acta Mathematicae Applicatae Sinica (2003-12-01) 19: 621-630 , December 01, 2003

###
*Abstract*

In this paper, a Markovian risk model is developed, in
which the occurrence of the claims is described by a point
process {*N(t)*}
_{t≥0}
with *N(t)* being the number of
jumps of a Markov chain during the interval [0,
*t*]. For the model, the
explicit form of the ruin probability Ψ(0) and the bound for the
convergence rate of the ruin probability Ψ(*u*) are given by using the generalized
renewal technique developed in this paper. Finally, we prove
that the ruin probability Ψ(*u*) is a linear combination of some
negative exponential functions in a special case when the claims
are exponentially distributed and the Markov chain has an
intensity matrix (*q*_{ij})_{i,j∈E} such that
*q*_{m} = *q*_{m1} and
*q*_{i} = *q*_{i(i+1)}, 1 ≤
*i* ≤ *m*−1.

## Infinite circulants and their properties

### Acta Mathematicae Applicatae Sinica (1995-07-01) 11: 280-284 , July 01, 1995

In recent years diverse literatures have been published on circulants (cf. [2] and the references cited therein). In this paper we consider the infinite analogues of circulant and random infinite circulant, and their connectivities and hamiltonian properties are discussed. Especially we answer a question of [4] in the case of infinite (undirected) circulants, and some results on random infinite circulants are also obtained.

## Boundary Value Problems for Singular Second-Order Functional Differential Equations

### Acta Mathematicae Applicatae Sinica (2002-06-01) 18: 249-254 , June 01, 2002

###
*Abstract*

Positive solutions to the boundary value problem,
$$
\left\{ {\begin{array}{*{20}l}
{{{y}\ifmmode{''}\else$''$\fi = - f{\left( {x,y{\left( {w{\left( x \right)}} \right)}} \right)},} \hfill} & {{0 < x < 1,} \hfill} \\
{{\alpha y{\left( x \right)} - \beta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \xi {\left( x \right)},} \hfill} & {{a \leqslant x \leqslant 0,} \hfill} \\
{{\gamma y{\left( x \right)} + \delta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \eta {\left( x \right)},} \hfill} & {{1 \leqslant x \leqslant b,} \hfill} \\
\end{array} } \right.
$$
are obtained by applying the Schauder fixed point theorem, where *w*(*x*) is a continuous function defined on [0, 1] and *f*(*x, y*) is a function defined on (0, 1)×(0, ∞), which satisfies certain restrictions and may have singularity at *y*=0. The result corrects and improves an existence theorem due to Erbe and Kong^{[1]}.

## Fixed Design Nonparametric Regression with Truncated and Censored Data

### Acta Mathematicae Applicatae Sinica (2003-06-01) 19: 229-238 , June 01, 2003

###
*Abstract*

In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function estimators.

## Spectral method for Zakharov equation with periodic boundary conditions

### Acta Mathematicae Applicatae Sinica (1989-09-01) 5: 279-288 , September 01, 1989

This paper describes the spectral method for numerically solving Zakharov equation with periodic boundary conditions. This method is spectral method for spatial variable and difference method for time variable. We make error estimation of approximate solution and prove the convergence of spectral method. We had given the convergence rate. Also, we prove the stability of approximate method for initial values.

## A new detecting method for conditions of existence of Hopf bifurcation

### Acta Mathematicae Applicatae Sinica (1995-01-01) 11: 79-93 , January 01, 1995

A new detecting method for the conditions of existence of the Hopf bifurcation is given in terms of the coefficients of the characteristic polynomial at the equilibrium by using the Hopf bifurcation theory and matrix theory. The method is available and important for the study of the existence of the Hopf bifurcation for higher differential equations which often occur in biological models, chemical models, epidemiological models, and models of AIDS.