共查询到20条相似文献,搜索用时 15 毫秒
1.
Vladimir S. Korolyuk 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(5):383-394
We study weak convergence of increment processes with embedded Markov chain switching in a series scheme. The limit process is a Lévy process where the jump part is a compound Poisson process. A result concerning the rate of convergence is also given. This study is motivated by risk theory and its applications. 相似文献
2.
邹东雅 《数学物理学报(A辑)》1992,(2)
关于两指标过程的Lévy Markov性,[2]证明了:对于广义Brownian Sheet和广义OUP_2,对适当的DR_+,有: 那里充分利用了过程的轨道连续性及正态系的一个性质:独立性等价于不相关性,[2]的这个结果使[1]中结果 (对一般的两指标Markov过程成立)对此特殊过程得到改进,本文的结果是:对于随机连续的独立增量过程(即两指标Lévy过程),对具有分段光滑边界的D∈B_+,有:由于两指标Lévy过程以广义Brownian Sheet,广义OUP_2及Poisson单为特例,故此结果推广了[2]的结果,而方法不同于[2] 相似文献
3.
We consider a finite time horizon optimal stopping of a regime-switching Lévy process. We prove that the value function of the optimal stopping problem can be characterized as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman variational inequalities. 相似文献
4.
Julien Fageot Michael Unser John Paul Ward 《Applied and Computational Harmonic Analysis》2017,42(1):21-36
In this paper, we study the Besov regularity of Lévy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for general Lévy white noises. Then, we focus on two subclasses of noises: compound Poisson and symmetric-α-stable (including Gaussian), for which we make more precise statements. Before measuring regularity, we show that the question is well-posed; we prove that Besov spaces are in the cylindrical σ-field of the space of generalized functions. These results pave the way to the characterization of the n-term wavelet approximation properties of stochastic processes. 相似文献
6.
Mariko Arisawa 《偏微分方程通讯》2013,38(7):617-624
The periodic homogenization of the integro-differential equation (PIDE) with the Lévy operator with the alpha-stable density, is studied in this paper. The formal asymptotic expansion method is employed to derive the cell problem, the ergodic problem for the Lévy operator without the second-order uniformly elliptic term. The effective equation is then obtained by using the result of the ergodic problem. Finally, the formal argument is justified rigorously by the perturbed test function method. 相似文献
7.
We study the optimal dividend problem in the dual model where dividend payments can only be made at the jump times of an independent Poisson process. In this context, Avanzi et al. (2014) solved the case with i.i.d. hyperexponential jumps; they showed the optimality of a (periodic) barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level. In this paper, we generalize the results for a general spectrally positive Lévy process with additional terminal payoff/penalty at ruin, and also solve the case with classical bail-outs so that the surplus is restricted to be nonnegative. The optimal strategies as well as the value functions are concisely written in terms of the scale function. Numerical results are also given. 相似文献
8.
9.
Steven N. Evans 《Journal of Theoretical Probability》1989,2(2):209-259
This paper is the first study of the sample path behavior of processes with stationary independent increments taking values in a nondiscrete, locally compact, metrizable, totally disconnected Abelian group. After some preparatory results of independent interest we give a general integral criterion for a deterministic function to be a local modulus of right-continuity for the paths of the process and then study the sets of fast and slow points where the local growth of the process is anomalously large or small. We establish the lim sup behavior for the sequence of first exit times from a collection of concentric balls for an arbitrary process and show that no deterministic function can act as an exact lower envelope. Under appropriate conditions similar results hold for the related sojourn time sequence. We consider various candidates for measuring the variation of the paths of the process, show that they exist and coincide in our situation, and then determine the common value for a general process. Using earlier results we calculate the Hausdorff and packing dimensions of the image of an interval, exhibit the correct Hausdorff measure for this set, and establish a dichotomy that classifies measure functions into those that lead to a zero packing measure for the image and those that lead to an infinite packing measure. Lastly, we prove some uniform dimension results, which bound the dimension of the image of a set in terms of the dimension of the set itself. These results hold almost surely for all sets simultaneously. 相似文献
10.
Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional Lévy processes are defined by integrating the infinite interval kernel w.r.t. a general Lévy process. In this article we define fractional Lévy processes using the com pact interval representation. We prove that the fractional Lévy processes presented via different integral transformations have the same finite dimensional distributions if and only if they are fractional Brownian motions. Also, we present relations between different fractional Lévy processes and analyze the properties of such processes. A financial example is introduced as well. 相似文献
11.
In this paper we investigate the limit distribution of the functions of independent triangular arrays Xnj, 1≤j≤k(n), n≥1. According to LeCam's theorem, if f belongs to the class of functionsPD[0,2] (which is slightly weaker than the assumptions that f(0)=0, and f has the second derivative at zero), then the distribution
of
is shift convergent. He also gives the explicit form of the characteristic function of the limit infinitely divisible distribution.
We consider the class of functionsPD[0,1] and prove a similar statement. Since in the definition of the sequence of centering constants the truncation points
depend only on the value of Xnj and not on the function f, this makes the analysis of the joint distribution of random variables in the above form considerably
easier. Also we analyze the process of partial sums
, 0≤u≤1. where f(x,t) is a parametric family of functions depending continuously on the parameter t. In the case of power
functions we give an explicit representation of the limit process in term of Poissonian integrals.
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II. Eger. Hungary. 1994. 相似文献
12.
We derive an explicit formula for the Jacobi field that is acting in an extended Fock space and corresponds to an (
-valued) Lévy process on a Riemannian manifold. The support of the measure of jumps in the Lévy–Khintchine representation for the Lévy process is supposed to have an infinite number of points. We characterize the gamma, Pascal, and Meixner processes as the only Lévy process whose Jacobi field leaves the set of finite continuous elements of the extended Fock space invariant. 相似文献
13.
We develop an approach to Malliavin calculus for Lévy processes from the perspective of expressing a random variable \(Y\) by a functional \(F\) mapping from the Skorohod space of càdlàg functions to \(\mathbb {R}\), such that \(Y=F(X)\) where \(X\) denotes the Lévy process. We also present a chain-rule-type application for random variables of the form \(f(\omega ,Y(\omega ))\). An important tool for these results is a technique which allows us to transfer identities proved on the canonical probability space (in the sense of Solé et al.) associated to a Lévy process with triplet \((\gamma ,\sigma ,\nu )\) to an arbitrary probability space \((\varOmega ,\mathcal {F},\mathbb {P})\) which carries a Lévy process with the same triplet. 相似文献
14.
LetX, Y be independent Lévy processes on the real line. AssumeX andY admit Lebesgue measure as a reference measure, thatP
0(X
t
>0)=c for allt>0 (or the weaker conditionP
0(X
t
>0)=c ast) and thatY
t
has a local time at points. We investigate the distribution of the local timeL
t
of (X, Y) on the positivex-axis. It turns out that, under the first hypothesis (which is in particular satisfied by planar Brownian motion), ifT is an independent exponential time, then the ratio ofL
T
to
T
, the local time on the entirex axis, is (generalized) arc-sine and independent of
T
, andL
T
has a Gamma distribution. We obtain then expressions for the distribution ofL
t
. In the case of Brownian motion, the formula involves parabolic cylinder functions. Under the weaker condition mentioned above, together with mild secondary hypotheses, we obtain an expression for the asymptotic distribution ofL
t
for larget.Research supported in part by NSF Grant DMS 91-01675. 相似文献
15.
In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging. 相似文献
16.
S. S. Sinelnikov 《Moscow University Mathematics Bulletin》2011,66(4):158-162
For a Lévy process X = (X
t
)0≤t<∞ we consider the time θ = inf{t ≥ 0: sup
s≤t
X
s
= sup
s≥0
X
s
}. We study an optimal approximation of the time θ using the information available at the current instant. A Lévy process being a combination of a Brownian motion with a drift
and a Poisson process is considered as an example. 相似文献
17.
Romuald Hervé Momeya Manuel Morales 《Methodology and Computing in Applied Probability》2016,18(1):107-135
Regime-switching models (RSM) have been recently used in the literature as alternatives to the Black-Scholes model. Several authors favor RSM as being more realistic since, by construction, they model those exogenous macroeconomic cycles against which asset prices evolve. In the context of derivatives pricing, these models lead to incomplete markets and therefore there exist multiple Equivalent Martingale Measures (EMM) yielding different pricing rules. A fair amount of literature (Buffington and Elliott, Int J Theor Appl Finance 40:267–282, 2002; Elliott et al., Ann Finance 1(4):23–432, 2005) focuses on conveniently choosing a family of EMM leading to closed-form formulas for option prices. These studies often make the assumption that the risk associated with the Markov chain is not priced. Recently, Siu and Yang (Acta Math Appl Sin Engl Ser 25(3):339–388, 2009), proposed an EMM kernel that takes into account all risk components of a regime-switching Black-Scholes model. In this paper, we extend the results and observations made in Siu and Yang (Acta Math Appl Sin Engl Ser 25(3):339–388, 2009) in order to include more general Lévy regime-switching models that allow us to assess the influence of jumps on the price of risk. In particular, numerical results are given for Regime-switching Jump-Diffusion and Variance-Gamma models. Also, we carry out a comparative analysis of the resulting option price formulas with existing regime-switching models such as Naik (J Financ 48:1969–1984, 1993) and Boyle and Draviam (Insur Math Econ 40:267–282, 2007). 相似文献
18.
《高校应用数学学报(A辑)》2016,(4)
对一般的Markov调制Lévy模型,利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法.进一步,为了改进期权定价的Fourier Cosine级数展开方法的计算精度,Fourier Cosine级数展开的对象进行了修正,获得了欧式期权价格的修正Fourier Cosine级数展开计算方法.此外,还将获得的方法应用于Markov调制Black-Scholes模型,Markov调制Merton跳扩散模型和Markov调制CGMY Lévy模型期权定价的计算.具体的数值计算说明:修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比,收敛速度要慢一些,但准确性却有很大的提高.特别是对Markov调制纯跳模型,效果更为显著. 相似文献
19.
20.
Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator. 相似文献