Quadratic backward stochastic differential equation
Some contributions to stochastic control and backward stochastic differential equations in finance.
... Black-Scholes-Barrenblat equation which is fully ...order stochastic target problem whose solution solves a 2BSDE and prove existence and uniqueness for general 2BSDEs in [86] with an undominated family of ...
162
MODEL UNCERTAINTY IN FINANCE AND SECOND ORDER BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
... by stochastic optimal control in the seminal paper [ 81 ...with quadratic growth ...to quadratic BSDEs. They also showed a deep link between quadratic growth and the BMO ...type ...
223
Forward and Backward Stochastic Differential Equations with normal constraint in law
... or backward) Stochastic Differential Equations (SDE) in the case where the constraint is on the law of the solution rather than on its ...their backward form in [4] in the scalar case and when ...
67
Backward Stochastic Differential Equations on Manifolds
... using differential ge- ometry tools, in particular by Arnaudon ([1]), Darling ([6]), Emery([10]), Kendall ([15]), Picard ([27] and [28]) or Thalmaier ([32] and [31]); note also the results of Estrade and Pontier ...
48
Partial Differential Equation and Noise
... (NLS) equation and the Korteweg - de Vries (KdV) ...Schrödinger equation is the modelling of the propagation of short light pulses in optical fibers, and the Korteweg - de Vries equation is used for ...
167
Stochastic graph partitioning: quadratic versus SOCP formulations
... For a formal proof of the equivalence between (Bi-SOCP) and (I) refer to [24]. It is clear that |T 0 | ≤ m(n − 2) thus the number of triangle constraints in (Bi-SOCP) is O(mn) instead of O(n 3 ). We can see that the ...
13
Linear Quadratic Zero-Sum Two-Person Differential Games
... linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati ...Riccati equation is not necessary for the existence of a closed-loop saddle ...
6
Strong existence and uniqueness for stochastic differential equation with Hölder drift and degenerate noise
... t , X t 2 , 0 ≤ t ≤ T ) adapted to the filtration gen- erated by the Brownian motion (W t , 0 ≤ t ≤ T ) which satisfies ( 1.1 ). Strong uniqueness means that if two processes satisfy this equation with the same ...
30
Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process
... 1. Introduction. 1.1. Objectives and motivations. This paper is devoted to the computa- tion of the invariant measure (denoted by ν) of ergodic stochastic processes which obey a stochastic ...
50
Backward Itô-Ventzell and stochastic interpolation formulae
... two-sided stochastic integral defined in ...two-sided stochastic integration calculus developed by Pardoux and Protter in [43] nor to any type of backward Itô-Ventzell ...
55
A cubature based algorithm to solve decoupled McKean-Vlasov Forward Backward Stochastic Differential Equations
... Objectives and organization of this paper. As a corollary of the discussion on the conditional system we can resume our objective as the approximation of Eφ(X T x ), where (X t x ) 0≤t≤T is the solution of ( 1.1 ) and ...
44
Day-ahead probabilistic forecast of solar irradiance: a Stochastic Differential Equation approach
... specific stochastic model, analytical or numerical methods are not applicable, which limits the resolution of some problems (like stochastic control ...
22
Conditional Monte Carlo Learning for Diffusions I: main methodology and application to backward stochastic differential equations
... October 6, 2020 Abstract We present a new algorithm based on a One-layered Nested Monte Carlo (1NMC) to simulate functionals U of a Markov process X. The main originality of the proposed methodology comes from the fact ...
28
Stochastic Homogenization of Reflected Stochastic Differential Equations
... Those stochastic processes are involved in the probabilistic representation of second order partial differential equations in half-space with Neumann boundary conditions (see [17] for an insight of the ...
35
Partial differential equation models in macroeconomics
... 1 Introduction Macroeconomics is the study of large economic systems. Most commonly this system is the economy of a country. But it may also be a more complex system such as the world as a whole, comprised of a large ...
19
A veraging principle for stochastic differential equations
... Veretennikov (1990) On large deviations in the averaging principle for stochas- tic differential equations with periodic coefficients. Veretennikov (1991) On the averaging prin[r] ...
57
A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation.
... [6] Viorel Barbu, Michael R¨ockner, and Francesco Russo. The stochastic porous media equation with multiplicative noise in the whole space. Preprint hal-00921597. [7] Viorel Barbu, Michael R¨ockner, and ...
68
Multidimensional stochastic differential equations with distributional drift
... of stochastic differential equations with generalized coefficients, it is difficult to quote them all: in particular, we refer to the case when b is a measure, [4, 7, 18, ...solving stochastic ...
26
The stochastic porous media equation in $\R^d$
... [18] H ¨ormander, L., 1963. Linear partial differential operators. Die Grundlehren der mathematischen Wissenschaften, Bd. 116. Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-G ...
27
Tanaka's equation on the circle and stochastic flows
... Tanaka’s equation on an oriented graph with two edges and two ...this equation to flows of kernels, we show that the laws of the flows of kernels K solutions of Tanaka’s equation can be classified by ...
35