Optimal importance sampling for the Laplace transform of exponential Brownian functionals

2016 ◽  
Vol 53 (2) ◽  
pp. 531-542 ◽  
Author(s):  
Je Guk Kim
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Performance Analysis ◽  
Laplace Transform ◽  
Importance Sampling ◽  
Pricing Model ◽  
Asymptotically Optimal ◽  
Closed Form Solutions ◽  
The Laplace Transform ◽  
Exponential Brownian Functionals

Abstract We present an asymptotically optimal importance sampling for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals which plays a prominent role in many disciplines. To this end we utilize the theory of large deviations to reduce finding an asymptotically optimal importance sampling measure to solving a calculus of variations problem. Closed-form solutions are obtained. In addition we also present a path to the test of regularity of optimal drift which is an issue in implementing the proposed method. The performance analysis of the method is provided through the Dothan bond pricing model.

Reliability Assessment of Power System Using Importance Sampling Technique Based on Layer Optimization Simulation

2011 ◽  
Vol 88-89 ◽  
pp. 554-558 ◽  
Author(s):  
Bin Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Power System ◽  
Importance Sampling ◽  
System Reliability ◽  
Sampling Method ◽  
Sampling Technique ◽  
Test System ◽  
Importance Sampling Method ◽  
Importance Sampling Technique

An improved importance sampling method with layer simulation optimization is presented in this paper. Through the solution sequence of the components’ optimum biased factors according to their importance degree to system reliability, the presented technique can further accelerate the convergence speed of the Monte-Carlo simulation. The idea is that the multivariate distribution’ optimization of components in power system is transferred to many steps’ optimization based on importance sampling method with different optimum biased factors. The practice is that the components are layered according to their importance degree to the system reliability before the Monte-Carlo simulation, the more forward, the more important, and the optimum biased factors of components in the latest layer is searched while the importance sampling is carried out until the demanded accuracy is reached. The validity of the presented is verified using the IEEE-RTS79 test system.

An Importance Sampling Approach for Time-Dependent Reliability

2011 ◽  
Author(s):  
Amandeep Singh ◽  
Zissimos P. Mourelatos ◽  
Efstratios Nikolaidis
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Random Process ◽  
Importance Sampling ◽  
Sampling Technique ◽  
Process Time ◽  
Cumulative Probability ◽  
Repairable Systems ◽  
Importance Sampling Method ◽  
True Value

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. The reliability usually degrades with time increasing the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time. In this article, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available which provide an upper bound to the true reliability which may overestimate the true value considerably. The traditional Monte-Carlo simulation is accurate but computationally expensive. A computationally efficient importance sampling technique is presented to calculate the cumulative probability of failure for random dynamic systems excited by a stationary input random process. Time series modeling is used to characterize the input random process. A detailed example demonstrates the accuracy and efficiency of the proposed importance sampling method over the traditional Monte Carlo simulation.

scholarly journals Approximating the Laplace transform of the sum of dependent lognormals

2016 ◽  
Vol 48 (A) ◽  
pp. 203-215 ◽  
Author(s):  
Patrick J. Laub ◽  
Søren Asmussen ◽  
Jens L. Jensen ◽  
Leonardo Rojas-Nandayapa
Keyword(s):  
Monte Carlo ◽  
Laplace Transform ◽  
Taylor Expansion ◽  
Multivariate Normal ◽  
Numerical Examples ◽  
Quasi Monte Carlo ◽  
Error Factor ◽  
The Laplace Transform ◽  
Laplace Transform Inversion ◽  
Mean Vector

AbstractLet (X1,...,Xn) be multivariate normal, with mean vector 𝛍 and covariance matrix 𝚺, and letSn=eX1+⋯+eXn. The Laplace transform ℒ(θ)=𝔼e-θSn∝∫exp{-hθ(𝒙)}d𝒙 is represented as ℒ̃(θ)I(θ), where ℒ̃(θ) is given in closed form andI(θ) is the error factor (≈1). We obtain ℒ̃(θ) by replacinghθ(𝒙) with a second-order Taylor expansion around its minimiser 𝒙*. An algorithm for calculating the asymptotic expansion of 𝒙*is presented, and it is shown thatI(θ)→ 1 as θ→∞. A variety of numerical methods for evaluatingI(θ) is discussed, including Monte Carlo with importance sampling and quasi-Monte Carlo. Numerical examples (including Laplace-transform inversion for the density ofSn) are also given.

Performance analysis of an improved 3-D PET Monte Carlo simulation and scatter correction

2002 ◽  
Vol 49 (1) ◽  
pp. 83-89 ◽  
Author(s):  
C.H. Holdsworth ◽  
C.S. Levin ◽  
M. Janecek ◽  
M. Dahlbom ◽  
E.J. Hoffman
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Performance Analysis ◽  
Scatter Correction

A Financial Protection Strategy for Families That Have a Child With Down Syndrome

2018 ◽  
Vol 29 (1) ◽  
pp. 91-102
Author(s):  
Gao Niu ◽  
Jeyaraj Vadiveloo ◽  
Cary Lakenbach
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Down Syndrome ◽  
Daily Life ◽  
Longevity Risk ◽  
Financial Protection ◽  
Pricing Model ◽  
Effect Factor ◽  
Protection Strategy ◽  
Monte Carlo Simulation Model

Families that have a child with Down syndrome (DS) are facing financial challenges due to the increased life expectancy and daily life dependencies that he or she experiences. This article uses pediatric findings to supplement child mortality impairment assumptions and proposes a combination annuity pricing model to explore an annuity solution for families that have a child with DS. A Markov chain Monte Carlo simulation model is constructed with features such as a fixed death benefit, return of premium, different premium payment patterns, and the widowhood effect factor. The results indicate that such a product is generally affordable for families that have a child with DS to cover their child’s longevity risk and increased dependency needs.

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