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The aim of this paper is to study asymptotic geometric properties almost surely or/and in probability of extreme order statistics of an i.i.d. random field (potential) indexed by sites of multidimensional lattice cube, the volume of which…
The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant…
We present the high-temperature series for a nearest-neighbor model with O(2) symmetry on a simple cubic lattice with the most general single-site potential. In particular, the magnetic susceptibility and the second-moment correlation…
In this article, we study a class of lattice random variables in the domain of attraction of an $\alpha$-stable random variable with index $\alpha \in (0,2)$ which satisfy a truncated fractional Edgeworth expansion. Our results include…
Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential…
In this paper, we study the topological asymptotic expansion of a topology optimisation problem that is constrained by the Poisson equation with the design/shape variable entering through the right hand side. Using an averaged adjoint…
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…
We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Levy-type process, we derive a family of asymptotic…
In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization…
We consider two canonical Bayesian mechanism design settings. In the single-item setting, we prove tight approximation ratio for anonymous pricing: compared with Myerson Auction, it extracts at least $\frac{1}{2.62}$-fraction of revenue;…
In this paper we establish local estimates for the first passage time of a subordinator under the assumption that it belongs to the Feller class, either at zero or infinity, having as a particular case the subordinators which are in the…
Asymptotics for Dickman's number theoretic function $\rho(u)$, as $u \rightarrow \infty$, were given de Bruijn and Alladi, and later in sharper form by Hildebrand and Tenenbaum. The perspective in these works is that of analytic number…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
ATSM are widely applied for pricing of bonds and interest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open question. First, the standard approach to ATSM uses the…
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process…
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…
We consider the problem of determining the L\'evy exponent in a L\'evy model for asset prices given the price data of derivatives. The model, formulated under the real-world measure $\mathbb P$, consists of a pricing kernel…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…