Mostrando recursos 1 - 20 de 614

  1. Multivariate risk processes with interacting intensities

    Bäuerle, Nicole; Grübel, Rudolf
    The classical models in risk theory consider a single type of claim. In the insurance business, however, several business lines with separate claim arrival processes appear naturally, and the individual claim processes may not be independent. We introduce a new class of models for such situations, where the underlying counting process is a multivariate continuous-time Markov chain of pure-birth type and the dependency of the components arises from the fact that the birth rate for a specific claim type may depend on the number of claims in the other component processes. Under certain conditions, we obtain a fluid limit, i.e. a functional law of large numbers for these processes. We...

  2. Steady-state analysis of a multiserver queue in the Halfin-Whitt regime

    Gamarnik, David; Momčilović, Petar
    We consider a multiserver queue in the Halfin-Whitt regime: as the number of servers n grows without a bound, the utilization approaches 1 from below at the rate Θ(1/√n). Assuming that the service time distribution is lattice valued with a finite support, we characterize the limiting scaled stationary queue length distribution in terms of the stationary distribution of an explicitly constructed Markov chain. Furthermore, we obtain an explicit expression for the critical exponent for the moment generating function of a limiting stationary queue length. This exponent has a compact representation in terms of three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times. Interestingly,...

  3. Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

    Piera, Francisco J.; Mazumdar, Ravi R.; Guillemin, Fabrice M.
    In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of Rn. We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary...

  4. A characterization of the first hitting time of double integral processes to curved boundaries

    Touboul, Jonathan; Faugeras, Olivier
    The problem of finding the probability distribution of the first hitting time of a double integral process (DIP) such as the integrated Wiener process (IWP) has been an important and difficult endeavor in stochastic calculus. It has applications in many fields of physics (first exit time of a particle in a noisy force field) or in biology and neuroscience (spike time distribution of an integrate-and-fire neuron with exponentially decaying synaptic current). The only results available are an approximation of the stationary mean crossing time and the distribution of the first hitting time of the IWP to a constant boundary. We generalize these results and find an analytical formula for the first...

  5. Importance sampling and the two-locus model with subdivided population structure

    Griffiths, Robert C.; Jenkins, Paul A.; Song, Yun S.
    The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance-sampling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel sampling distributions for the two-locus model. We consider the case with subdivided population structure, as well as the classic case with only a single population. In the latter case we also consider the importance-sampling proposal distributions suggested by Fearnhead and Donnelly (2001), and show that their two-locus distributions generally differ from ours. In the case of the infinitely-many-alleles...

  6. Using systematic sampling selection for Monte Carlo solutions of Feynman-Kac equations

    Gentil, Ivan; Rémillard, Bruno
    While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to `systematic sampling' in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.

  7. Large deviation estimates of the crossing probability for pinned Gaussian processes

    Caramellino, Lucia; Pacchiarotti, Barbara
    The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in n fixed points at n fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motions and m-fold integrated Brownian motion. As an application, the asymptotic behavior of the exit probability is studied and used for the practical purpose of the numerical computation, via Monte Carlo methods, of the hitting probability up to a given time of the unpinned process.

  8. Exponential utility indifference valuation in two Brownian settings with stochastic correlation

    Frei, Christoph; Schweizer, Martin
    We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the value VB of the exponential utility maximization problem with the claim B as random endowment. This yields an explicit formula for the indifference value b of B at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended. The reason why all this works is that, after a...

  9. Index policies for discounted bandit problems with availability constraints

    Dayanik, Savas; Powell, Warren; Yamazaki, Kazutoshi
    A multiarmed bandit problem is studied when the arms are not always available. The arms are first assumed to be intermittently available with some state/action-dependent probabilities. It is proven that no index policy can attain the maximum expected total discounted reward in every instance of that problem. The Whittle index policy is derived, and its properties are studied. Then it is assumed that the arms may break down, but repair is an option at some cost, and the new Whittle index policy is derived. Both problems are indexable. The proposed index policies cannot be dominated by any other index policy over all multiarmed bandit problems considered here. Whittle indices are...

  10. Optimal selection policies for a sequence of candidate drugs

    Charalambous, C.; Gittins, J. C.
    Pharmaceutical companies have to face huge risks and enormous costs of production before they can produce a drug. Efficient allocation of resources is essential to help in maximizing profits. Yu and Gittins (2007) described a model and associated software for determining efficient allocations for a preclinical research project. This is the starting point for this paper. We provide explicit optimal policies for the selection of successive candidate drugs for two restricted versions of the Yu and Gittins (2007) model. To some extent these policies are likely to be applicable to the unrestricted model.

  11. Length and surface area estimation under smoothness restrictions

    Pateiro-López, Beatriz; Rodríguez-Casal, Alberto
    The problem of estimating the Minkowski content L0(G) of a body G ⊂ Rd is considered. For d = 2, the Minkowski content represents the boundary length of G. It is assumed that a ball of radius r can roll inside and outside the boundary of G. We use this shape restriction to propose a new estimator for L0(G). This estimator is based on the information provided by a random sample, taken on a square containing G, in which we know whether a sample point is in G or not. We obtain the almost sure convergence rate for the proposed estimator.

  12. Power diagrams and interaction processes for unions of discs

    Møller, Jesper; Helisová, Kateřina
    We study a flexible class of finite-disc process models with interaction between the discs. We let U denote the random set given by the union of discs, and use for the disc process an exponential family density with the canonical sufficient statistic depending only on geometric properties of U such as the area, perimeter, Euler-Poincaré characteristic, and the number of holes. This includes the quermass-interaction process and the continuum random-cluster model as special cases. Viewing our model as a connected component Markov point process, and thereby establishing local and spatial Markov properties, becomes useful for handling the problem of edge effects when only U is observed within a bounded observation window....

  13. Monte Carlo methods for sensitivity analysis of Poisson-driven stochastic systems, and applications

    Bordenave, Charles; Torrisi, Giovanni Luca
    We extend a result due to Zazanis (1992) on the analyticity of the expectation of suitable functionals of homogeneous Poisson processes with respect to the intensity of the process. As our main result, we provide Monte Carlo estimators for the derivatives. We apply our results to stochastic models which are of interest in stochastic geometry and insurance.

  14. Exact Monte Carlo simulation of killed diffusions

    Casella, Bruno; Roberts, Gareth O.
    We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

  15. Nonexplosion of a class of semilinear equations via branching particle representations

    Chakraborty, Santanu; López-Mimbela, Jose Alfredo
    We consider a branching particle system where an individual particle gives birth to a random number of offspring at the place where it dies. The probability distribution of the number of offspring is given by pk, k = 2, 3, .... The corresponding branching process is related to the semilinear partial differential equation ∂u / ∂t = Au(t, x) + ∑k=2pk(x)uk(t, x) for x ∈ Rd, where A is the infinitesimal generator of a multiplicative semigroup and the pks, k = 2, 3, ..., are nonnegative functions such that ∑kpk = 1. We obtain sufficient conditions for the existence of global positive solutions to semilinear equations of this form. Our results extend previous work by...

  16. Identifiability of a Markovian model of molecular evolution with Gamma-distributed rates

    Allman, Elizabeth S.; Ané, Cécile; Rhodes, John A.
    Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips of the tree. Rate heterogeneity is present in most real data sets and is accounted for by the use of flexible mixture models where each site is allowed its own rate. Very little has been rigorously established concerning the identifiability of the models currently in common use in data analysis, although nonidentifiability was proven for a semiparametric model and an incorrect proof of identifiability was published for a general parametric model (GTR + Γ + I). Here...

  17. On the number of jumps of random walks with a barrier

    Iksanov, Alex; Möhle, Martin
    Let S0 := 0 and Sk := ξ1 + ··· + ξk for k ∈ N := {1, 2, ...}, where {ξk : k ∈ N} are independent copies of a random variable ξ with values in N and distribution pk := P{ξ = k}, k ∈ N. We interpret the random walk {Sk : k = 0, 1, 2, ...} as a particle jumping to the right through integer positions. Fix n ∈ N and modify the process by requiring that the particle is bumped back to its current state each time a jump would bring the particle to a state larger than or equal to n. This constraint defines an increasing...

  18. Local properties of random mappings with exchangeable in-degrees

    Hansen, Jennie C.; Jaworski, Jerzy
    In this paper we investigate the `local' properties of a random mapping model, Tn, which maps the set {1, 2, ..., n} into itself. The random mapping Tn, which was introduced in a companion paper (Hansen and Jaworski (2008)), is constructed using a collection of exchangeable random variables D̂1, ..., D̂n which satisfy ∑i=1ni = n. In the random digraph, Gn, which represents the mapping Tn, the in-degree sequence for the vertices is given by the variables D̂1, D̂2, ..., D̂n, and, in some sense, Gn can be viewed as an analogue of the general independent degree models from random graph theory. By local properties we mean the distributions of random mapping characteristics related to a given vertex v of Gn -...

  19. The generalized perpetual American exchange-option problem

    Wong, Shek-Keung Tony
    This paper revisits a general optimal stopping problem that often appears as a special case in some finance applications. The problem is essentially of the same form as the investment-timing problem of McDonald and Siegel (1986) in which the underlying processes are two correlated geometric Brownian motions (GBMs) with drifts less than the discount rate. By contrast, we attempt to analyze the underlying optimal stopping problem to its full generality without imposing any restriction on the drifts of the GBMs. By extending the first passage time approach of Xia and Zhou (2007) to the current context, we manage to obtain a complete and explicit characterization of the solution to the...

  20. Malliavin differentiability of the Heston volatility and applications to option pricing

    Alòs, Elisa; Ewald, Christian-Oliver
    We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.