On the integral of geometric Brownian motion
نویسندگان
چکیده
منابع مشابه
On the Integral of Geometric Brownian Motion
Abstract. This paper studies the law of any power of the integral of geometric Brownian motion over any finite time interval. As its main results, two integral representations for this law are derived. This is by enhancing the Laplace transform ansatz of [Y] with complex analytic methods, which is the main methodological contribution of the paper. The one of our integrals has a similar structur...
متن کامل1 Geometric Brownian motion
where X(t) = σB(t) + μt is BM with drift and S(0) = S0 > 0 is the intial value. We view S(t) as the price per share at time t of a risky asset such as stock. Taking logarithms yields back the BM; X(t) = ln(S(t)/S0) = ln(S(t))− ln(S0). ln(S(t)) = ln(S0) +X(t) is normal with mean μt + ln(S0), and variance σ2t; thus, for each t, S(t) has a lognormal distribution. As we will see in Section 1.4: let...
متن کاملSimulating Brownian motion ( BM ) and geometric Brownian
2) and 3) together can be summarized by: If t0 = 0 < t1 < t2 < · · · < tk, then the increment rvs B(ti) − B(ti−1), i ∈ {1, . . . k}, are independent with B(ti) − B(ti−1) ∼ N(0, ti − ti−1) (normal with mean 0 and variance ti − ti−1). In particular, B(ti) − B(ti−1) is independent of B(ti−1) = B(ti−1)−B(0). If we only wish to simulate B(t) at one fixed value t, then we need only generate a unit no...
متن کاملExact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
In this paper Lie symmetry analysis is applied to find new solution for Fokker Plank equation of geometric Brownian motion. This analysis classifies the solution format of the Fokker Plank equation.
متن کاملOn the Validity of the Geometric Brownian Motion Assumption
The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices, and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2003
ISSN: 0001-8678,1475-6064
DOI: 10.1239/aap/1046366104