# Cristina CostantiniUniversità degli Studi G. d'Annunzio Chieti e Pescara | UNICH · Department of Economics

Cristina Costantini

PhD

## About

29

Publications

1,332

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278

Citations

## Publications

Publications (29)

We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each "side", under optimal conditions. Our conditions are optimal in the sense that, in the case of a polygonal domain, they reduce to the conditions of Dai and Williams (1996), which...

In this paper, we propose a new model for the joint evolution of the inflation rate, the Central Bank official interest rate and the short-term interest rate. Our model takes into account the fact that the Central Bank interest rate changes at random times, inflation is measured at fixed, regular times, while the short-term interest rate evolves es...

Bass and Pardoux (1987) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub-probability transition function, which turns out to be a key tool in proving uniqueness of Reflecting Brownian Motion in cones in Kwon and Williams (1991) and in Taylor and Williams (1993). By a different approach, we are able to prove an analogous reve...

We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation form...

We propose a new model for the joint evolution of the European inflation rate, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent claim and show that it has a unique solution. The contingent claim payoff may depend on all thre...

Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In this paper, the behavior in the interior is specified by a generator of a Markov process, and the constraints ar...

We consider stochastic differential equations with (oblique) reflection in a 2-dimensional domain that has a cusp at the origin, i.e. in a neighborhood of the origin has the form {(x1, x2): 0 < x1 ≤ δ0, ψ1(x1) < x2 < ψ2(x1)}, with ψ1(0) = ψ2(0) = 0, ψ1(0)′ = ψ2′(0) = 0. Given a vector field g of directions of reflection at the boundary points other...

The two-parameter Poisson-Dirichlet diffusion, recently introduced by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson-Dirichlet distribution and to certain Fleming-Viot processes. The additional parameter has been shown to regulate the clustering structure of the population, but is yet...

Let $E$ be a complete, separable metric space and $A$ be an operator on
$C_b(E)$. We give an abstract definition of viscosity sub/supersolution of the
resolvent equation $\lambda u-Au=h$ and show that, if the comparison principle
holds, then the martingale problem for $A$ has a unique solution. Our proofs
work also under two alternative definitions...

Many risk-neutral pricing problems proposed in the finance literature do not admit closed-form expressions and have to be dealt with by solving the corresponding partial integro-differential equation. Often, these PIDEs have singular diffusion matrices and coefficients that are not Lipschitz-continuous up to the boundary. In addition, in general, b...

European inflation and interest rates are closed related. In particular we consider the relationship among European inflation, European Central Bank official interest rate and short-term interest rate in a stochastic continuous time setting for the val- uation of inflation derivatives. We model the state variables in two different time scales and w...

Diffusion approximations are obtained for space inhomogeneous linear transport models with reflection boundary conditions. The collision kernel is not required to satisfy any balance condition and the scattering kernel on the boundary is general enough to include all examples of boundary conditions known to the authors (with conservation of the num...

We study the sensitivity, with respect to a time dependent domain
Ds,{\cal D}_s,
of expectations of functionals of a diffusion process stopped at the exit from
Ds{\cal D}_s
or normally reflected at the boundary of
Ds.{\cal D}_s.
We establish a differentiability result and give an explicit expression for the gradient that allows the gradient to b...

We consider the solution X=(Xt)t⩾0 of a time-inhomogeneous stochastic differential equation and the exit time τ by (t,Xt)t⩾0 of the time–space domain D. We prove the differentiability of expectations of functionals of X stopped at τ, with respect to the domain D: these results extend those in the literature, known in particular by the analysts for...

The main discretization schemes for diffusion processes, both unrestricted and reflecting in a hyper-rectangle, are considered. For every discretized path, an `antithetic' path is obtained by changing the sign of the driving random variables, which are chosen symmetric. It is shown that, under suitable monotonicity assumptions on the coefficients a...

For statistical models admitting a sufficient, transitive sequence of one-dimensional statistics, Brown, Cohen and Strawderman proved in 1979 that, under simple conditions verified in many examples, all Bayes sequential tests are monotone. We extend the definition of monotone test to higher dimension in a suitable way, and show that the same result...

The aim of this paper is to approximate the expectation of a large class of functionals of the solution (X,ξ) of a stochastic differential equation with normal reflection in a piecewise smooth domain of ℝ d . This also yields a Monte Carlo method for solving partial differential problems of parabolic type with mixed boundary conditions. The approxi...

We consider the problem of the optimal duration of a burn-in experiment for n identical units with conditionally exponential life-times of unknown parameter Λ. The problem is formulated as an optimal stopping problem for a suitably defined two-dimensional continuous-time Markov process. By exploiting monotonicity properties of the statistical model...

We consider the problem of the optimal duration of a burn-in experiment for n identical units with conditionally exponential life-times of unknown parameter Λ. The problem is formulated as an optimal stopping problem for a suitably defined two-dimensional continuous-time Markov process. By exploiting monotonicity properties of the statistical model...

We study the behavior of the nonlinear Markov process associated to the Boltzmann equation under both hyperbolic and parabolic space-time scalings. In the first case the limit of the process is the solution of an o.d.e. with vector field given by a solution of the Euler equation, while in the second case the limit of the process, in the incompressi...

The Skorohod oblique reflection problem for (D, Γ, w) (D a general domain in ℝd
, Γ(x),x∈∂D, a convex cone of directions of reflection,w a function inD(ℝ+,ℝd
)) is considered. It is first proved, under a condition on (D, Γ), corresponding to Γ(x) not being simultaneously too large and too much skewed with respect to ∂D, that given a sequence {w
n}...

Consider a stochastic process consisting of the pair of a position and a velocity, in a piecewise $\mathscr{L}^1 d$-dimensional domain. In the interior of the domain the dynamics are assigned by a potential and by random changes of the velocity occurring at exponentially distributed times, according to a probability distribution which may depend on...

A continuous measure-valued model is obtained as the limit of discrete finite-dimensional Markov processes describing the evolution of a population of interacting cells (classified by their DNA content), as the initial number of individuals diverges and the DNA production unit tends independently to zero. The limit is identified by a nonlinear evol...

This paper deals with the estimate of errors introduced by finite sampling in Monte Carlo evaluation of functionals of stochastic processes. To this end we introduce a metric d over the space of probability measures which induces a topology finer than the weak topology. For any two measures [mu], v, this metric allows to bound /vb<[mu],f> - <v,f>/v...

This paper presents two main results: first, a Liapunov type criterion for the existence of a stationary probability distribution for a jump Markov process; second, a Liapunov type criterion for existence and tightness of stationary probability distributions for a sequence of jump Markov processes. If the corresponding semigroups TN(t) converge, un...

The problem is motivated by stochastic modeling of chemical reactions, but it is studied in a general framework. The fluctuations of a sequence of jump Markov processes around their deterministic limit are considered. It is shown that, if the deterministic limit has an equilibrium point which is at least k-asymptotically stable, the sequence of flu...