scholarly journals The moment problem for some Wiener functionals: corrections to previous proofs (with an appendix by H. L. Pedersen)

2005 ◽  
Vol 42 (03) ◽  
pp. 851-860 ◽  
Author(s):  
Per Hörfelt
Keyword(s):  
Brownian Motion ◽  
Moment Problem ◽  
Geometric Brownian Motion ◽  
Geometric Inequalities ◽  
Gauss Space ◽  
The Moment

In this paper, we describe a class of Wiener functionals that are ‘indeterminate by their moments’, that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen.

scholarly journals The moment problem for some Wiener functionals: corrections to previous proofs (with an appendix by H. L. Pedersen)

2005 ◽  
Vol 42 (3) ◽  
pp. 851-860 ◽  
Author(s):  
Per Hörfelt
Keyword(s):  
Brownian Motion ◽  
Moment Problem ◽  
Geometric Brownian Motion ◽  
Geometric Inequalities ◽  
Gauss Space ◽  
The Moment

In this paper, we describe a class of Wiener functionals that are ‘indeterminate by their moments’, that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen.

scholarly journals Asymptotics for the discrete-time average of the geometric Brownian motion and Asian options

2017 ◽  
Vol 49 (2) ◽  
pp. 446-480 ◽  
Author(s):  
Dan Pirjol ◽  
Lingjiong Zhu
Keyword(s):  
Brownian Motion ◽  
Discrete Time ◽  
Moment Generating Function ◽  
Mathematical Finance ◽  
Geometric Brownian Motion ◽  
Time Averaging ◽  
Asian Options ◽  
Time Average ◽  
Averaging Time ◽  
The Moment

Abstract The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-time averaging in the Black–Scholes model, with both fixed and floating strike.

scholarly journals Geometric Brownian motion with affine drift and its time-integral

2021 ◽  
Vol 395 ◽  
pp. 125874
Author(s):  
Runhuan Feng ◽  
Pingping Jiang ◽  
Hans Volkmer
Keyword(s):  
Brownian Motion ◽  
Geometric Brownian Motion ◽  
Time Integral

The moment problem on perfect hypergroups

2016 ◽  
Vol 29 (2) ◽  
pp. 232-236
Author(s):  
A. S. Okb El Bab ◽  
Hossam A. Ghany
Keyword(s):  
Moment Problem ◽  
The Moment

scholarly journals HOLDER-EXTENDIBLE EUROPEAN OPTION: CORRECTIONS AND EXTENSIONS

2015 ◽  
Vol 56 (4) ◽  
pp. 359-372 ◽  
Author(s):  
PAVEL V. SHEVCHENKO
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Real Life ◽  
Option Price ◽  
Geometric Brownian Motion ◽  
Fixed Amount ◽  
Underlying Asset ◽  
Closed Form Solutions ◽  
Pricing Options ◽  
Interest Rate Volatility

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.

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