scholarly journals THE POTENTIAL APPROACH IN PRACTICE

2018 ◽  
Vol 21 (03) ◽  
pp. 1850021
Author(s):  
T. KLUGE ◽  
L. C. G. ROGERS
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Process ◽  
Particle Filtering ◽  
Sequential Monte Carlo ◽  
Market Prices ◽  
Potential Models ◽  
Potential Approach ◽  
Finite State ◽  
Interest Rate Derivative

This paper studies the fitting of Markov chain potential models to interest-rate derivative prices in four currencies simultaneously, using sequential Monte Carlo methodology (particle filtering). The potential approach starts from some Markov process which is supposed to drive the random observations, and there have been many studies where this Markov process is taken to be a diffusion; fewer studies have worked from a finite-state Markov chain, and this seems to be the first study to attempt to fit such models to data. With the available data, we show impressive agreement of the fitted models with market prices.

scholarly journals A sequential Bayesian approach for the estimation of the age–depth relationship of Dome Fuji ice core

2015 ◽  
Vol 2 (3) ◽  
pp. 939-968
Author(s):  
S. Nakano ◽  
K. Suzuki ◽  
K. Kawamura ◽  
F. Parrenin ◽  
T. Higuchi
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Sequential Monte Carlo ◽  
Ice Core ◽  
Posterior Distributions ◽  
Metropolis Method ◽  
Depth Relationship ◽  
Relationship Of ◽  
Thinning Process

Abstract. A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is mainly determined by the accumulation of snow at the site of the ice core and the thinning process due to the horizontal stretching and vertical compression of ice layers. However, since neither the accumulation process nor the thinning process are fully understood, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated from age markers and δ18O data. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, in which the sequential Monte Carlo (SMC) method is combined with the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning processes are computed using the Metropolis method, in which the likelihood is obtained with the SMC method. Meanwhile, the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.

Combining Particle Filters with MH Samplers

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Particle Filtering ◽  
Likelihood Function ◽  
Mcmc Methods ◽  
Acceptance Probability ◽  
Likelihood Functions ◽  
Approximate Likelihood ◽  
Special Case

This chapter argues that in order to conduct Bayesian inference, the approximate likelihood function has to be embedded into a posterior sampler. It begins by combining the particle filtering methods with the MCMC methods, replacing the actual likelihood functions that appear in the formula for the acceptance probability in Algorithm 5 with particle filter approximations. The chapter refers to the resulting algorithm as PFMH algorithm. It is a special case of a larger class of algorithms called particle Markov chain Monte Carlo (PMCMC). The theoretical properties of PMCMC methods were established in Andrieu, Doucet, and Holenstein (2010). Applications of PFMH algorithms in other areas of econometrics are discussed in Flury and Shephard (2011).

Sufficient optimality conditions for control-limit policy in a semi-Markov process

1976 ◽  
Vol 13 (2) ◽  
pp. 400-406 ◽  
Author(s):  
I. Gertsbach
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Optimality Conditions ◽  
Hazard Rate ◽  
The State ◽  
Control Limit ◽  
Sufficient Optimality Conditions ◽  
Finite State ◽  
Semi Markov Process ◽  
Rate Property

A finite-state semi-Markov process (SMP) with penalties is considered. A property which is similar to an increasing-hazard-rate property for a Markov chain is defined for an SMP. The SMP is controlled by shifts from the state Ei to immediately after a transition has occurred. Conditions are given which guarantee that the optimal stationary Markovian policy belongs to a subclass of control-limit policies.

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