scholarly journals On the double Laplace transform of the truncated variation of a Brownian motion with drift

2016 ◽  
Vol 19 (1) ◽  
pp. 281-292
Author(s):  
Rafał Marcin Łochowski
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Independent Interest ◽  
Brownian Motion With Drift ◽  
Double Laplace Transform ◽  
Truncated Variation

The aim of this paper is to find a formula for the double Laplace transform of the truncated variation of a Brownian motion with drift. In order to find the double Laplace transform, we also prove some identities for the Brownian motion with drift, which may be of independent interest.

scholarly journals The Integral of the Supremum Process of Brownian Motion

2009 ◽  
Vol 46 (2) ◽  
pp. 593-600 ◽  
Author(s):  
Svante Janson ◽  
Niclas Petersson
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Explicit Formula ◽  
Local Time ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Excursion Theory ◽  
Double Laplace Transform ◽  
The Laplace Transform ◽  
Supremum Process

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

scholarly journals Double-Barrier Parisian Options

2011 ◽  
Vol 48 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Angelos Dassios ◽  
Shanle Wu
Keyword(s):  
Brownian Motion ◽  
Markov Model ◽  
Laplace Transform ◽  
Mathematical Finance ◽  
Important Application ◽  
Double Barrier ◽  
Parisian Options ◽  
Brownian Motion With Drift ◽  
The Laplace Transform ◽  
Excursion Time

In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

scholarly journals Parisian Time of Reflected Brownian Motion with Drift on Rays and Its Application in Banking

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 127
Author(s):  
Angelos Dassios ◽  
Junyi Zhang
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Liquidity Risk ◽  
Finite Collection ◽  
Recursive Method ◽  
Simulation Algorithm ◽  
Reflected Brownian Motion ◽  
Brownian Motion With Drift ◽  
The Laplace Transform ◽  
First Time

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper was motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit. We reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results to the existing literature.

scholarly journals Double-Barrier Parisian Options

2011 ◽  
Vol 48 (01) ◽  
pp. 1-20 ◽  
Author(s):  
Angelos Dassios ◽  
Shanle Wu
Keyword(s):  
Brownian Motion ◽  
Markov Model ◽  
Laplace Transform ◽  
Mathematical Finance ◽  
Important Application ◽  
Double Barrier ◽  
Parisian Options ◽  
Brownian Motion With Drift ◽  
The Laplace Transform ◽  
Excursion Time

In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

scholarly journals The Integral of the Supremum Process of Brownian Motion

2009 ◽  
Vol 46 (02) ◽  
pp. 593-600
Author(s):  
Svante Janson ◽  
Niclas Petersson
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Explicit Formula ◽  
Local Time ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Excursion Theory ◽  
Double Laplace Transform ◽  
The Laplace Transform ◽  
Supremum Process

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

scholarly journals Parisian Time of Reflected Brownian Motion With Drift on Rays

2020 ◽  
Author(s):  
Angelos Dassios ◽  
Junyi Zhang
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Liquidity Risk ◽  
Finite Collection ◽  
Recursive Method ◽  
Simulation Algorithm ◽  
Reflected Brownian Motion ◽  
Brownian Motion With Drift ◽  
The Laplace Transform ◽  
First Time

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper is motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit, we reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results with the existing literature.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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