不规则波抛物型缓底坡波动方程

使用Kubo近似，导出了不规则波抛物型缓底坡波动方程的折射绕射联合模型。对不规则波抛物型缓底坡波动方程进行数值模拟，并对结与实验进行比较。不规则波抛物型缓底坡波动方程能很好地描述波浪传播过程中的变化，由此，可以预测波浪在传播过程中受到地形及波浪间相互用作而发生的变化。     

坝体泄洪深孔明槽段体型研究

通过对三峡泄洪深孔明槽段体型试验研究 ,比较了明槽段不同抛物线型的压力特性和空化特性 ,并提出了明槽段陡槽方案。研究结果表明 :陡槽方案较之抛物线方案 ,压力特性和水流空化特性有显著改善。陡槽方案是免空化的 ,而抛物线方案较难达到免除空化 ;并且陡槽方案对有压段压力及空化特性 ,以及泄流能力均没有影响。因此 ,对于高速水流条件下的明槽段体型 ,陡槽方案是一种较为适宜的布置形式。     

非线性抛物型缓坡方程的数值模拟

参考Lo对MNLS方程中非线性项的处理方法,但不转换到频域求解,同时采用Li修正的非线性弥散关系,对非线性抛物型缓坡方程在复数域进行数值模拟,并分别在Berkhoff椭圆地形及淹没圆形浅滩地形验证了该模型,得到了较好的结果。此模型可以有效地模拟非线性波浪问题。此非线性项的处理方法使得数值计算过程中不需迭代求解,同时减少了边界周期性的限制,易于操作编程,提高了计算效率。     

EFFICIENT PRICING OF BARRIER OPTIONS AND CREDIT DEFAULT SWAPS IN LÉVY MODELS WITH STOCHASTIC INTEREST RATE

Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of Lévy models, the Heston model, and other affine models. Similar deformations were used in one‐factor Lévy models to price options with barrier and lookback features and credit default swaps (CDSs). In the present paper, we generalize this approach to models, where the dynamics of the assets is modeled as , where X is a Lévy process, and the interest rate is stochastic. Assuming that X and r are independent, and , the infinitesimal generator of the pricing semigroup in the model for the short rate, satisfies weak regularity conditions, which hold for popular models of the short rate, we develop a variation of the pricing procedure for Lévy models which is almost as fast as in the case of the constant interest rate. Numerical examples show that about 0.15 second suffices to calculate prices of 8 options of same maturity in a two‐factor model with the error tolerance and less; in a three‐factor model, accuracy of order 0.001–0.005 is achieved in about 0.2 second. Similar results are obtained for quanto CDS, where an additional stochastic factor is the exchange rate. We suggest a class of Lévy models with the stochastic interest rate driven by 1–3 factors, which allows for fast calculations. This class can satisfy the current regulatory requirements for banks mandating sufficiently sophisticated credit risk models.