American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

Abstract

We consider the Heston model with the stochastic interest rate of Cox–Ingersoll–Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. Time-derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time discretization of a Markov-modulated Lévy model. Options in this sequence are solved using an iteration method based on the Wiener–Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff–Schwartz method and Medvedev–Scaillet asymptotic method is demonstrated.     

Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces

The stochastic integrals of M- type 2 Banach valued random functions w.r.t. compensated Poisson random measures introduced in (Rüdiger, B., 2004, In: Stoch. Stoch. Rep., 76, 213–242.) are discussed for general random functions. These are used to solve stochastic integral equations driven by non Gaussian Lévy noise on such spaces. Existence and uniqueness of the path wise solutions are proven under local Lipshitz conditions for the drift and noise coefficients on M-type 2 as well as general separable Banach spaces. The continuous dependence of the solution on the initial data as well as on the drift and noise coefficients are shown. The Markov properties for the solutions are analyzed.     

Necessary conditions for optimal singular stochastic control problems

In this paper, necessary conditions of optimality, in the form of a maximum principle, are obtained for singular stochastic control problems. This maximum principle is derived for a state process satisfying a general stochastic differential equation where the coefficient associated to the control process can be dependent on the state, extending earlier results of the literature.     

Stochastic partial functional differential equations with locally monotone coefficients,locally Lipschitz non-linearity and delay

In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results.     

基于随机共振和微纳传感器阵列的六氟化硫检测方法研究

建立了一种基于随机共振和微纳传感器阵列的六氟化硫气体检测方法.使用两个360 μm极间距离的微纳传感器构成的阵列结合随机共振算法,在室温常压,相对湿度70%的条件下检测3.0～24 g/m3 SF6气体及纯SF6气体,以信噪比极大值实现各浓度SF6气体的区分.传感器工作于微电离平衡状态,检测过程中无有害气体产生,安全性较高.为检验该方法的实用性,依据国家标准在温度20 ℃、相对湿度70%和常压条件下模拟现场检测3.0～12 g/m3SF6气体,结果表明: 本方法具有较好的重复性和实用性.     

基于周期调节的随机共振算法对化学弱信号的检测研究

提出了一种新的随机共振算法,通过对系统的周期进行调节以实现系统的共振.讨论了实现共振的系统参数,并对模拟信号和拉曼光谱实验信号进行了处理.结果表明,该方法不仅可方便地用于弱化学信号的处理,克服检出信号的滞后现象,而且对不同噪声水平的信号均有良好的适用性.     

X-ray study of volatile Ni(II), Cu(II), and Pd(II) complexes of β-ketoimine pivalyltrifluoroacetone

Synthesis of volatile complexes based on -ketoimine pivalyltrifluoroacetone, C(CH₃)₃C(NH)CH₂COCF₃, is described. The general formula of the complexes is M(L)₂, where M = Cu, Ni, Pd. Complexes of this kind with Ni and Pd were obtained for the first time. The Cu and Pd complexes were found to be isostructural. A comprehensive crystal-chemical study showed that all structures are molecular and built of trans-complexes. The central atom has a square plane environment. The average M-O and M-N distances are nearly equal in all compounds: 1.84 , 1.92 , and 1.98 for Ni, Cu, and Pd complexes, respectively; the mean values of the O-M-N chelate angles are 93.4°, 91.9°, and 92.7°, respectively.Original Russian Text Copyright © 2004 by I. A. Baidina, G. I. Zharkova, N. V. Pervukhina, S. A. Gromilov, and I. K. IgumenovTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 713–722, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

铁岭煤中重金属元素的赋存形态及其在热解过程中的挥发行为研究

采用密度分离、脱灰处理和逐级化学提取等间接方法,考察了铁岭煤中Pb, Cr, Co, Ni, V五个重金属元素的宏观结合形态,并在Φ25mm小型石英流化床反应装置上考察了上述五个重金属元素在热解过程中的挥发行为。研究发现,铁岭煤中Pb, Cr, Co, Ni, V均主要与非黄铁矿类矿物质相伴生, 且高达40%～60%赋存在硅酸盐类矿物质中。Pb的碳酸盐结合态和有机束缚的离子可交换态600℃前即可分解转化,而其硫化物和硫酸盐结合态在较高的热解温度下才能分解挥发；Co、Ni的硫化物和硫酸盐结合态在高温下可部分转换为有机结合的离子可交换态；而Cr、V的硫化物和硫酸盐结合态在高温下部分转化生成了新的热稳定相。在500℃～900℃范围内,Pb属半挥发性元素,Cr, Co, Ni, V属难挥发性元素。微量元素的挥发性极大地受其伴生环境、共存活泼元素等的影响,硅铝酸盐类矿物质对重金属元素的挥发有一定的抑制作用。