Related papers: Cylindrical stochastic integration and application…
This note studies a certain stochastic evolution equation in the space of probability measures, including existence and uniqueness results. A solution of this equation gives rise, in a natural way, to an interest rate term structure model,…
We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on \Ito stochastic differential equations in infinite dimensional spaces, and prove strong and weak…
Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic…
In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic…
This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo…
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of…
We develop a unified framework for modeling multiple term structures arising in financial, insurance, and energy markets, adopting an extended Heath-Jarrow-Morton (HJM) approach under the real-world probability. We study market viability…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
We introduce a stochastic integral with respect to cylindrical L\'evy processes with finite $p$-th weak moment for $p\in [1,2]$. The space of integrands consists of $p$-summing operators between Banach spaces of martingale type $p$. We…
We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in…
We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the…
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…
The partial stochastic realization of periodic processes from finite covariance data has recently been solved by Lindquist and Picci based on convex optimization of a generalized entropy functional. The meaning and the role of this…
We consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general…
This paper addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…
We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…