摘要:

In 1973, Black and Scholes showed that a portfolio made up of shares of an asset A, whose price varies as a geometric Brownian motion, and shares of an asset B, whose price per share is functionally dependent on the price per share of A could be manipulated to be riskless, and designed to achieve any given rate of return on investment

ISSN:0736-2994    

DOI:10.1080/07362998408809024

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362998408809025

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

Probabilistic origin of the laws of Mechanics and Relativity: In a diffusion with exclusion principle, the brownian bridges propagate pressure wavelets which interfere and make wave packets of which the group velocity Vgtends to equal the expansion velocity v of the Huygens sphere envelope of these wavelets. This convergence Vg> v due to the strong large numbers law involves the Galilean and Lorentz groups, the limit Vg=v is reached on monochromatic waves and stationary states.

ISSN:0736-2994    

DOI:10.1080/07362998408809026

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

Let xtbe a diffusion process satisfying a stochastic differential equation of the formwhere [Wtilde] is an n-dimensional Brownian motion. Let the observed process ytbe related to xtby,where W is one dimensional Brownian motion Independent of [Wtilde]. The measure γ is a random counting measure independent of [Wtilde] and W. The problem is to find the conditional probability of the process xtgiven the observed path yt0. The results of absolute continuity of measures are used to derive a stochastic differential equation for the required conditional probability .Our results are easily extended to the case where the process xtis governed by a stochastic differential equation also containing jump process, as indicated in Remark 1. Our results also cover the filter equation given by Gertner [4], Di Masi [5] and Pardoux [6] . Further, Zakaitype equation (linear stochastic partial differential equation) corresponding to the systems considered by Shiryayev [3] and Snyder [9], which are of Kushner type (nonlinear stochastic partial differential equation), also follow from our main results . Finally, some open questions arising from this work are discussed in Remark 2

ISSN:0736-2994    

DOI:10.1080/07362998408809027

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

Random differential equations in Banach spaces without solutions are considered. Some density results are established.

ISSN:0736-2994    

DOI:10.1080/07362998408809028

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362998408809023

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor