| 1. |
- Abramowicz, Konrad, et al.
(författare)
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Stratified Monte Carlo quadrature for continuous random fields
- 2015
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Ingår i: Methodology and Computing in Applied Probability. - New York : Springer Science+Business Media B.V.. - 1387-5841 .- 1573-7713. ; 17:1, s. 59-72
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behavior is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the H¨older class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.
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| 2. |
- Asmussen, S, et al.
(författare)
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Performance analysis with truncated heavy-tailed distributions
- 2005
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Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1573-7713 .- 1387-5841. ; 7:4, s. 439-457
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U boolean AND K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than EU. We study the compound Poisson ruin probability psi(u) or, equivalently, the tail P(W > u) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of psi(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times, and compare the results to different approximations of psi(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we investigate the asymptotics as K -> infinity of the asymptotic exponential decay rate gamma = gamma((K)) in a more general truncated Levy process setting, and give a discussion of some of the implications for the approximations.
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| 3. |
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| 4. |
- Bondesson, Lennart, 1944-
(författare)
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On the Lévy measure of the lognormal and logCauchy distributions
- 2002
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Ingår i: Methodology and Computing in Applied Probability. - : Springer. - 1387-5841 .- 1573-7713. ; 4:3, s. 243-256
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Tidskriftsartikel (refereegranskat)abstract
- The densities of the Lévy measure and the Thorin measure of the standard lognormal distribution are approximated and presented in graphs. Moreover, the behavior of these densities at 0 and ∞ is studied. Laplace and saddlepoint approximations are used. The infinite divisibility of the standard logCauchy distribution is given some attention in passing.
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| 5. |
- Canhanga, Betuel, 1980-, et al.
(författare)
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Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility
- 2017
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Ingår i: Methodology and Computing in Applied Probability. - : Springer. - 1387-5841 .- 1573-7713. ; 19:4, s. 1075-1087
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Tidskriftsartikel (refereegranskat)abstract
- Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).
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| 6. |
- Grage, Halfdan, et al.
(författare)
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Level crossing prediction with neural networks
- 2010
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Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1573-7713 .- 1387-5841. ; 63:Online First, s. 623-645
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Tidskriftsartikel (refereegranskat)abstract
- A level crossing predictor or alarm system with prediction horizon k is said to be optimal if it, at time t detects that an upcrossing will occur at time t + k, with a certain high probability and simultaneously gives a minimum number of false alarms. For a Gaussian stationary process, the optimal level crossing predictor can be explicitly specified in terms of the predicted value of the process itself and of its derivative. To the authors knowledge this simple optimal solution has not been used to any substantial degree. In this paper it is shown how a neural network can be trained to approximate an optimal alarm system arbitrarily well. As in other methods of parametrization, the choice of model structure, as well as an appropriate representation of data, are crucial for a good result. Comparative studies are presented for two Gaussian ARMA-processes, for which the optimal predictor can be derived theoretically. These studies confirm that a properly trained neural network can indeed approximate an optimal alarm system quite well – with due attention paid to the problems of model structure and representation of data. The technique is also tested on a strongly non-Gaussian Duffing process with satisfactory results.
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| 7. |
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| 8. |
- Hössjer, Ola
(författare)
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Spatial Autocorrelation for Subdivided Populations with Invariant Migration Schemes
- 2014
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Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1387-5841 .- 1573-7713. ; 16:4, s. 777-810
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Tidskriftsartikel (refereegranskat)abstract
- For populations with geographic substructure and selectively neutral genetic data, the short term dynamics is a balance between migration and genetic drift. Before fixation of any allele, the system enters into a quasi equilibrium (QE) state. Hossjer and Ryman (2012) developed a general QE methodology for computing approximations of spatial autocorrelations of allele frequencies between subpopulations, subpopulation differentiation (fixation indexes) and variance effective population sizes. In this paper we treat a class of models with translationally invariant migration and use Fourier transforms for computing these quantities. We show how the QE approach is related to other methods based on conditional kinship coefficients between subpopulations under mutation-migration-drift equilibrium. We also verify that QE autocorrelations of allele frequencies are closely related to the expected value of Moran's autocorrelation function and treat limits of continuous spatial location (isolation by distance) and an infinite lattice of subpopulations. The theory is illustrated with several examples including island models, circular and torus stepping stone models, von Mises models, hierarchical island models and Gaussian models. It is well known that the fixation index contains information about the effective number of migrants. The spatial autocorrelations are complementary and typically reveal the type of migration (local or global).
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| 9. |
- Kuljus, Kristi, et al.
(författare)
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On the Accuracy of the MAP Inference in HMMs
- 2016
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Ingår i: Methodology and Computing in Applied Probability. - : Springer Netherlands. - 1387-5841 .- 1573-7713. ; 18:3, s. 597-627
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Tidskriftsartikel (refereegranskat)abstract
- In a hidden Markov model, the underlying Markov chain is usually unobserved. Often, the state path with maximum posterior probability (Viterbi path) is used as its estimate. Although having the biggest posterior probability, the Viterbi path can behave very atypically by passing states of low marginal posterior probability. To avoid such situations, the Viterbi path can be modified to bypass such states. In this article, an iterative procedure for improving the Viterbi path in such a way is proposed and studied. The iterative approach is compared with a simple batch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi state path is more efficient and it has several advantages over the batch approach. The same iterative algorithm for improving the Viterbi path can be used when it is possible to reveal some hidden states and estimating the unobserved state sequence can be considered as an active learning task. The batch approach as well as the iterative approach are based on classification probabilities of the Viterbi path. Classification probabilities play an important role in determining a suitable value for the threshold parameter used in both algorithms. Therefore, properties of classification probabilities under different conditions on the model parameters are studied.
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| 10. |
- Leonenko, Nikolai N., et al.
(författare)
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SupOU-based and Related Fractal Activity Time Models for Risky Assets with Dependence
- 2023
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Ingår i: Methodology and Computing in Applied Probability. - : Springer. - 1387-5841 .- 1573-7713.
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Tidskriftsartikel (refereegranskat)abstract
- We propose several new models in ecophysics known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. We derive solutions of option Greeks and compare with those in the Black-Scholes model. We analyse perfor-mance of delta hedging strategy using simulated time series data and verify that hedging errors are biased particularly for long-range dependence cases. We also apply underlying model calibration on S&P 500 index (SPX) and the U.S./Euro rate, and implement delta hedging on SPX options.
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