Occupation times and other accumulation processes

1977 ◽  
Vol 9 (2) ◽  
pp. 196-197
Author(s):  
J. Horowitz
Keyword(s):  
Occupation Times

THE FEYNMAN–KAC FORMULA AND PRICING OCCUPATION TIME DERIVATIVES

1999 ◽  
Vol 02 (02) ◽  
pp. 153-178 ◽  
Author(s):  
JULIEN-N. HUGONNIER
Keyword(s):  
Brownian Motion ◽  
Time Derivative ◽  
Occupation Time ◽  
Barrier Options ◽  
Occupation Times

In this paper, we undertake a study of occupation time derivatives that is derivatives for which the pay-off is contingent on both the terminal asset's price and one of its occupation times. To this end we use a formula of M. Kac to compute the joint law of Brownian motion and one of its occupation times. General pricing formulas for occupation time derivatives are established and it is shown that any occupation time derivative can be continuously hedged by a controlled portfolio of the basic securities. We further study some examples of interest including cumulative barrier options and discuss some numerical implementations.

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

Limit theorems on occupation times for perturbed random walks

1996 ◽  
Vol 15 (2-3) ◽  
pp. 103-122
Author(s):  
Mei Wang
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
Occupation Times

scholarly journals First point measurements of ice-sheet thickness change in Antarctica

1998 ◽  
Vol 27 ◽  
pp. 125-129 ◽  
Author(s):  
Gordon S. Hamilton ◽  
Ian M. Whillans ◽  
Peter J. Morgan
Keyword(s):  
Ice Sheet ◽  
Sheet Thickness ◽  
Snow Accumulation ◽  
Repeated Measurements ◽  
Occupation Times ◽  
Thickness Change ◽  
Global Positioning ◽  
First Results ◽  
Ice Stream B

Ice-sheet thickening or thinning rates in Antarctica are measured using the “coffee-can” or “submergence velocity” method. in this, repeated measurements of the positions of firn anchors are obtained using the global positioning system (GPS). The thickness change is (lie difference between vertical velocity so obtained and long-term rate of snow accumulation. Minor corrections for firn settling and downslopc motion are made. The technique avoids difficulties of short-term fluctuations in snowfall or snow den-sification. The result for Byrd Station is near balance, -0.004 (0.022) ma−1, and for the Dragon, just outboard of Ice Stream B, thinning at -0.096 (0.044) ma−1. Uncertainties with these first results are mainly due to the short occupation times during the first GPS surveys.

scholarly journals Pricing and risk management under multivariate switching models

2021 ◽  
Author(s):  
Atousa Assadihaghi
Keyword(s):  
Monte Carlo ◽  
Continuous Time ◽  
Value At Risk ◽  
Markov Models ◽  
Risk Measures ◽  
Occupation Times ◽  
Taylor Expansions ◽  
Switching Regime ◽  
Switching Models ◽  
Analytic Expressions

The objective of this thesis is to provide a simulations-free approximation to the price of multivariate derivatives and for the calculation of risk measures like Value at Risk (VaR). The first chapters are dedicated to the pricing of multivariate derivatives. In particular we focus on multivariate derivatives under switching regime Markov models. We consider the cases of two and three states of the switching regime Markov model, and derive analytic expressions for the first and second order moments of the occupation times of the continuous-time Markov process. Then we use these expressions to provide approximations for the derivative prices based on Taylor expansions. We compare our closed form approximations with Monte Carlo simulations. In the last chapter we also provide a simulations-free approximation for the VaR under a switching regime model with two states. We compare these VaR estimations with those obtained using Monte Carlo.

scholarly journals Occupation Times for Markov-Modulated Brownian Motion

2012 ◽  
Vol 49 (02) ◽  
pp. 549-565 ◽  
Author(s):  
Lothar Breuer
Keyword(s):  
Brownian Motion ◽  
First Passage Time ◽  
Passage Time ◽  
Laplace Transforms ◽  
Occupation Times ◽  
First Passage ◽  
Scale Functions ◽  
Positive Variation ◽  
Markov Modulated

In this paper we determine the distributions of occupation times of a Markov-modulated Brownian motion (MMBM) in separate intervals before a first passage time or an exit from an interval. We derive the distributions in terms of their Laplace transforms, and we also distinguish between occupation times in different phases. For MMBMs with strictly positive variation parameters, we further propose scale functions.

scholarly journals On occupation times in the red of Lévy risk models

2020 ◽  
Vol 92 ◽  
pp. 17-26
Author(s):  
David Landriault ◽  
Bin Li ◽  
Mohamed Amine Lkabous
Keyword(s):  
Occupation Times ◽  
Risk Models

scholarly journals A Continuous-Time Random Walk Extension of the Gillis Model

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1431
Author(s):  
Gaia Pozzoli ◽  
Mattia Radice ◽  
Manuele Onofri ◽  
Roberto Artuso
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Hitting Times ◽  
Occupation Times ◽  
Theoretical Predictions ◽  
Normal Diffusion ◽  
Heavy Tailed ◽  
The One ◽  
Waiting Periods

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations.

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