Quantization based recursive importance sampling

نویسندگان

  • Noufel Frikha
  • Abass Sagna
چکیده

We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and functional) optimal quantization with Newton-Raphson zero search procedure. Our approach can be seen as a robust and automatic deterministic counterpart of recursive importance sampling by means of stochastic approximation algorithm which, in practice, may require tuning and a good knowledge of the payoff function in practice. Moreover, unlike recursive importance sampling procedures, the proposed methodology does not rely on simulations so it is quite generic and can come along on the top of Monte Carlo simulations. We first emphasize on the consistency of quantization for designing an importance sampling algorithm for both multi-dimensional distributions and diffusion processes. We show that the induced error on the optimal change of measure is controlled by the mean quantization error. We illustrate the effectiveness of our algorithm by pricing several options in a multi-dimensional and infinite dimensional framework.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weight functions for signal reconstruction based on level crossings

Although the level crossing concept has been the subject of intensive investigation over the last few years, certain problems of great interest remain unsolved. One of these concern is distribution of threshold levels. This paper presents a new threshold level allocation schemes for level crossing based on nonuniform sampling. Intuitively, it is more reasonable if the information rich regions o...

متن کامل

Quantization Effects in Digital Filters

When a digital filter is implemented on a computer or with special-purpose hardware, errors and constraints due to finite word length are unavoidable. These quantization effects must be considered, both in deciding what register length is needed for a given filter implementation and in choosing between several possible implementations of the same filter design, which will be affected differentl...

متن کامل

On Parameter Tying by Quantization

The maximum likelihood estimator (MLE) is generally asymptotically consistent but is susceptible to overfitting. To combat this problem, regularization methods which reduce the variance at the cost of (slightly) increasing the bias are often employed in practice. In this paper, we present an alternative variance reduction (regularization) technique that quantizes the MLE estimates as a post pro...

متن کامل

The effect of sampling and quantization on frequency estimation

The effect of sampling and quantization on frequency estimation for a single sinusoid is investigated. Cramér-Rao bound for 1 bit quantization is derived, and compared with the limit of infinite quantization. It is found that 1 bit quantization gives a slightly worse performance, however, with a dramatic increase of variance at certain frequencies. This can be avoided by using 4 times oversampl...

متن کامل

Approximation of Bounds on Mixed Level Orthogonal Arrays

Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays. The computational complexity of the terms involved in these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Monte Carlo Meth. and Appl.

دوره 18  شماره 

صفحات  -

تاریخ انتشار 2012