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Optimal simulation schemes for Levy driven stochastic differential equations
Levy-driven stochastic differential equations high order discretization schemes weak approximation regular variation
2012/4/28
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson a...
A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
Stochastic optimal control non-Markovian SDE second order BSDE G-expectation random G-expectation volatility uncertainty risk measure
2011/7/5
We study stochastic differential equations (SDEs) whose drift and
diffusion coefficients are path-dependent and controlled. We construct
a value process on the canonical path space, considered simul...
Information Theoretic Limits on Learning Stochastic Differential Equations
drift high dimensional vector interaction coefficients
2011/3/31
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector.
Applications of time-delayed backward stochastic differential equations to pricing, hedging and management of financial and insurance risks
backward stochastic differential equations participating contracts
2010/10/20
In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise when we want to find a ...
Picard approximation of stochastic differential equations and application to LIBOR models
Picard approximation stochastic differential equations application LIBOR models
2010/10/21
The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic di...
Strong Taylor approximation of stochastic differential equations and application to the Lévy LIBOR model
LIBOR models stochastic differential equations L´ evy pro-cesses perturbation Taylor approximation caps, swaptions
2010/11/1
In this article we develop a method for the strong approx-imation of stochastic differential equations (SDEs) driven by L´evy pro-cesses or general semimartingales. The main ingredients of our m...
Reflected backward stochastic differential equations and a class of non linear dynamic pricing rule
stochastic differential equations non linear dynamic pricing rule
2010/12/13
In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver $g$ is convex and has quadratic growth in i...