We study a hedging and pricing problem of a model where the price process of a risky asset has jumps with instantaneous feedback from the most recent asset price. We model these jumps with a doubly stochastic Poisson process with an intensity function depending on the current price. We find a closed form expression of the local risk minimization strategy using Föllmer and Schweizer decompositio...

We study the existence and uniqueness theorem for the nonlinear fractional mixed Volterra-Fredholm integrodifferential equation with nonlocal initial condition dx t /dt f t, x t , ∫ t 0 k t, s, x s ds, ∫1 0 h t, s, x s ds , x 0 ∫1 0 g s x s ds, where t ∈ 0, 1 , 0 < α < 1, and f is a given function. We point out that such a kind of initial conditions or nonlocal restrictions could play an intere...

The properties of the gauge invariant two-point quark Green's function are studied in the large-N c limit of two-dimensional QCD. The analysis is done by means of an exact integrodifferential equation. The Green's function is found to be infrared finite, with singularities in the momentum squared variable represented by an infinite number of threshold type branch points with a power-3/2, starti...

We show that for the originally ill-posed inverse problem of calibrating a localized jump-diffusion process to given option price data, Tikhonov regularization can be used to get a well-posed optimization problem. Furthermore we prove stability as well as convergence of the regularized parameters using the forward partial integrodifferential equation associated to the European call price. By pr...

Area and axial flow variations on rectilinear vortex tubes are considered. The state of the flow is characterized by two dependent variables, a core area, and an azimuthal circulation per unit length, which vary in time and in distance along the length of the tube. Nonlinear integrodifferential equations of motion for these variables are derived by taking certain integrals of the vorticity tran...

The aim of this work is to revisit viscosity solutions’ theory for second-order elliptic integrodifferential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen-Ishii’s Lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The pr...

The continuum limit of a recently-proposed model for charge transport in resonanttunneling semiconductor superlattices is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, supplemented by shock and entropy conditions. For appropriate parameter values, a time-periodic solution is found in numerical simulations of the model. An ...

We study properties of the solutions of a family of second order integrodifferential equations, which describe the large scale dynamics of a class of microscopic phase segregation models with particle conserving dynamics. We first establish existence and uniqueness as well as some properties of the instantonic solutions. Then we concentrate on formal asymptotic (sharp interface) limits. We argu...

A rigorous non-existence proof for runaway solutions in the finite-size model of the electron is given. Since a consistent point limit, such as the Lorentz-Dirac equation claims to be, should not exhibit features which are completely missing in the more general theory of finite extension, it is proposed that the point-like approximation of the finite-size theory be the integrodifferential formu...

By applying hybrid functions of general block-pulse functions and the second Chebyshev polynomials, integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of integrodifferential systems are derived. The numerical examples illustrate that the algorithms are valid.