scholarly journals Multidimensional BSDE with Poisson jumps of Osgood type

2019 ◽  
Vol 4 (2) ◽  
pp. 387-394 ◽  
Author(s):  
Yaya Sagna
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Finite Time ◽  
Existence And Uniqueness ◽  
Time Horizon ◽  
Linear Growth ◽  
Backward Stochastic Differential Equation ◽  
Uniqueness Of Solution ◽  
Poisson Jumps ◽  
Finite Time Horizon

AbstractThis paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.

scholarly journals Lp (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals

2014 ◽  
Vol 15 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Li-Shun Xiao ◽  
Sheng-Jun Fan ◽  
Na Xu
Keyword(s):  
Differential Equation ◽  
Weak Convergence ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Additional Assumption ◽  
Backward Stochastic Differential Equation ◽  
Time Interval ◽  
Time Intervals ◽  
Lipschitz Continuous ◽  
General Time

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equation in Lp (p ≥ 1). We first study the existence and uniqueness for Lp (p > 1) solutions by the method of convolution and weak convergence when the generator is monotonic in y and Lipschitz continuous in z both non-uniformly with respect to t. Then we obtain the existence and uniqueness for L1 solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.

BSDE with rcll reflecting barrier driven by a Lévy process

2020 ◽  
Vol 28 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Mohamed El Jamali ◽  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
American Option ◽  
Levy Process ◽  
Fair Price ◽  
Penalization Method ◽  
Uniqueness Of A Solution

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

Fractional anticipated BSDEs with stochastic Lipschitz coefficients

2018 ◽  
Vol 26 (3) ◽  
pp. 143-161
Author(s):  
Ahmadou Bamba Sow ◽  
Bassirou Kor Diouf
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Hurst Parameter ◽  
Uniqueness Of A Solution

Abstract In this paper, we deal with an anticipated backward stochastic differential equation driven by a fractional Brownian motion with Hurst parameter {H\in(1/2,1)} . We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and prove a comparison theorem in a specific case.

scholarly journals Lp-SOLUTIONS FOR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 12 (02) ◽  
pp. 1150016 ◽  
Author(s):  
SAÏD HAMADÈNE ◽  
ALEXANDRE POPIER
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Snell Envelope ◽  
Equation Problem ◽  
Class Of Functions ◽  
Uniqueness Of A Solution ◽  
Lp Solutions

This paper deals with the problem of existence and uniqueness of a solution for a backward stochastic differential equation (BSDE for short) with one reflecting barrier in the case when the terminal value, the generator and the obstacle process are Lp-integrable with p ∈ ]1, 2[. To construct the solution we use two methods: penalization and Snell envelope. As an application we broaden the class of functions for which the related obstacle partial differential equation problem has a unique viscosity solution.

Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Sadibou Aidara ◽  
Ahmadou Bamba Sow
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Levy Process ◽  
Uniqueness Of Solution ◽  
Time Interval ◽  
Poisson Measure ◽  
Doubly Stochastic

AbstractIn this work we deal with a anticipated backward doubly stochastic differential equation associated to a random Poisson measure. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients. The novelty of our result lies in the fact that we allow the time interval to be infinite.

NON-LIPSCHITZ STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTI-PARAMETER BROWNIAN MOTIONS

2006 ◽  
Vol 06 (03) ◽  
pp. 329-340 ◽  
Author(s):  
XICHENG ZHANG ◽  
JINGYANG ZHU
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Lebesgue Measure ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Gronwall’S Inequality

By proving an extension of nonlinear Bihari's inequality (including Gronwall's inequality) to multi-parameter and non-Lebesgue measure, in this paper we first prove by successive approximation the existence and uniqueness of solution of stochastic differential equation with non-Lipschitz coefficients and driven by multi-parameter Brownian motion. Then we study two discretizing schemes for this type of equation, and obtain their L2-convergence speeds.

Existence and Uniqueness of Positive Solutions of a Randomized Spruce Budworm Model

2013 ◽  
Vol 785-786 ◽  
pp. 1198-1202
Author(s):  
Yan Qiu Li ◽  
Hai Long Gao
Keyword(s):  
Differential Equation ◽  
North America ◽  
Lyapunov Function ◽  
Stochastic Differential Equation ◽  
Finite Time ◽  
Existence And Uniqueness ◽  
Spruce Budworm ◽  
Coniferous Forests ◽  
Western North America ◽  
Simple Assumption

Spruce Budworm is the most destructive defoliator of coniferous forests in Western North America .This paper discusses a randomized Spruce Budworm model with HollingIII Functional Response. Using results from lyapunov function, we show that the positive solution of the associated stochastic differential equation does not explode to infinity in a finite time under simple assumption .It is shown to improve existing results.

scholarly journals A Study on a New Class of Backward Stochastic Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ping He ◽  
Yong Ren ◽  
Defei Zhang
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
New Class ◽  
The Past ◽  
The Future ◽  
New Type

The existence and uniqueness for a new type of backward stochastic differential equation when the generator includes the values of solutions of the past, the present, and the future are obtained in this paper. An important comparison theorem for this sort of BSDEs is also proved.

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