Anticipated backward stochastic differential equations driven by the Teugels martingales

We are interested in this paper on reflected anticipated backward doubly stochastic differential equations (RABDSDEs) driven by teugels martingales associated with Levy process. We obtain the existence and uniqueness of solutions to these equations by means of the fixed-point theorem where the coefficients of these BDSDEs depend on the future and present value of the solution $\left( Y,Z\right)$. We also show the comparison theorem for a special class of RABDSDEs under some slight stronger conditions. The novelty of our result lies in the fact that we allow the time interval to be infinite.

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“…Zong (2014) [11] studied the previous anticipated BSDE driven by teugels martingale and obtained an existence and uniqueness theorem.…”

Section: Proofs Of Main Resultsmentioning

confidence: 99%

Anticipated backward doubly stochastic differential equations driven by teugels martingales with or without reflecting barrier

Saouli

Mansouri

2020

DEMR

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“…It is easy to see that (24)- (25) are ordinary differential equations, which exist the solutions as follows:…”

Section: Application To Financementioning

confidence: 99%

“…Now we fix some parameters to illustrate the numerical results about the optimal consumption problem. Figures 1 and 2 illustrate the changing situation of the solutions p 1 (⋅) and p 3 (⋅) of (24) and (25) with respect to t and p * 1 (0), respectively. If a 1 = a 2 = b 1 = b 2 = 0.1, and = = 0.2, then it shows obviously that p 1 (⋅) and p 3 (⋅) decrease with respect to t and increase with respect to p * 1 (0).…”

Section: Application To Financementioning

confidence: 99%

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Infinite horizon optimal control for mean‐field stochastic delay systems driven by Teugels martingales under partial information

Yang

2020

Optim Control Appl Methods

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Summary In this article, we discuss an infinite horizon optimal control of the stochastic system with partial information, where the state is governed by a mean‐field stochastic differential delay equation driven by Teugels martingales associated with Lévy processes and an independent Brownian motion. First, we show the existence and uniqueness theorem for an infinite horizon mean‐field anticipated backward stochastic differential equation driven by Teugels martingales. Then applying different approaches for the underlying system, we establish two classes of stochastic maximum principles, which include two necessary conditions and two sufficient conditions for optimality, under a convex control domain. Moreover, compared with the finite horizon optimal control, we add the transversality conditions to the two kinds of stochastic maximum principles. Finally, using the stochastic maximum principle II, we settle an infinite horizon optimal consumption problem driven by Teugels martingales associated with Gamma processes.

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“…In 2013, Yang and Elliott [20] derived the existence of solutions to one-dimensional anticipated BSDEs with continuous coefficients, and showed the existence and comparison results of the minimal solutions. Zong [21] discussed the existence and uniqueness of the solutions of anticipated BSDEs driven by the Teugels martingales and established the corresponding comparison theorem.…”

Section: Introductionmentioning

confidence: 99%

On anticipated backward stochastic differential equations with Markov chain noise

Yang

Elliott

2016

Stochastic Analysis and Applications

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In 2013, Lu and Ren [8] considered anticipated backward stochastic differential equations driven by finite state, continuous time Markov chain noise and established the existence and uniqueness of the solutions of these equations and a scalar comparison theorem. In this paper, we provide an estimate for their solutions and study the duality between these equations and stochastic differential delayed equations with Markov chain noise. Finally we derive another comparison theorem for these solutions depending only on the two drivers.

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Anticipated backward stochastic differential equations driven by the Teugels martingales

Cited by 9 publications

References 14 publications

Anticipated backward doubly stochastic differential equations driven by teugels martingales with or without reflecting barrier

Anticipated backward doubly stochastic differential equations driven by teugels martingales with or without reflecting barrier

Infinite horizon optimal control for mean‐field stochastic delay systems driven by Teugels martingales under partial information

On anticipated backward stochastic differential equations with Markov chain noise

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