We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically computed using the classical finite difference methods. We p...

*Correspondence: [email protected] 1Department of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan Full list of author information is available at the end of the article Abstract We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this ...

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence. We generalize the result to the case where the one-s...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically constructed using the classical finite difference methods. W...

In this paper, we consider the problem of approximating a sequence of n points by a line segment in such a way that the distance of each point from this segment is not greater than a given constant. Furthermore, the distance between the first(last) input point and the start(end)-point of the approximating segment must not be greater than the given constant. This is a sub-problem in solving unre...

The verification of many algorithms for calculating transcendental functions is based on polynomial approximations to these functions, often Taylor series approximations. However, computing and verifying approximations to the arctangent function are very challenging problems, in large part because the Taylor series converges very slowly to arctangent—a 57th-degree polynomial is needed to get th...

Dedicated to Professor Gad M. Landau, on the occasion of his 60th birthday

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence. We generalize the result to the case where the one-s...

We consider a multidimensional normally or obliquely reflected diffusion in smooth domain. approximate it by solutions of stochastic differential equations without reflection using the penalty method, that is, we term with an additional drift term. In existing literature, usually specific approximating sequence is provided to prove existence diffusion. this paper, provide general sufficient con...