共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square-integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the Föllmer–Schweizer decomposition of a square-integrable random variable working under partial information and we use this achievement to investigate the local risk-minimization approach for a semimartingale financial market model. 相似文献
2.
We study the well-posedness of general reflected BSDEs driven by a continuous martingale, when the coefficient f of the driver has at most quadratic growth in the control variable Z, with a bounded terminal condition and a lower obstacle which is bounded above. We obtain the basic results in this setting: comparison and uniqueness, existence, stability. For the comparison theorem and the special comparison theorem for reflected BSDEs (which allows one to compare the increasing processes of two solutions), we give intrinsic proofs which do not rely on the comparison theorem for standard BSDEs. This allows to obtain the special comparison theorem under minimal assumptions. We obtain existence by using the fixed point theorem and then a series of perturbations, first in the case where f is Lipschitz in the primary variable Y, and then in the case where f can have slightly-superlinear growth and the case where f is monotonous in Y with arbitrary growth. We also obtain a local Lipschitz estimate in BMO for the martingale part of the solution. 相似文献
3.
Over the past few years quadratic Backward Stochastic Differential Equations (BSDEs) have been a popular field of research. However there are only very few examples where explicit solutions for these equations are known. In this paper we consider a class of quadratic BSDEs involving affine processes and show that their solution can be reduced to solving a system of generalized Riccati ordinary differential equations. In other words we introduce a rich and flexible class of quadratic BSDEs which are analytically tractable, i.e. explicit up to the solution of an ODE. Our results also provide analytically tractable solutions to the problem of utility maximization and indifference pricing in multivariate affine stochastic volatility models. This generalizes univariate results of Kallsen and Muhle-Karbe (2010) and some results in the multivariate setting of Leippold and Trojani (2010) by establishing the full picture in the multivariate affine jump-diffusion setting. In particular we calculate the interesting quantity of the power utility indifference value of change of numeraire. Explicit examples in the Heston, Barndorff-Nielsen–Shephard and multivariate Heston setting are calculated. 相似文献
4.
ShengJun Fan Long Jiang DeJian Tian 《Stochastic Processes and their Applications》2011,121(3):427-440
This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of BSDEs with linear growth generators. Then, we establish a general comparison theorem for solutions of this kind of BSDEs with weakly monotonic and uniformly continuous generators. Finally, we give an existence and uniqueness result for solutions of this kind of BSDEs with uniformly continuous generators. 相似文献
5.
The aim of this paper is twofold. First, we extend the results of Matoussi et al. (2013) concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar to the ones in Crépey and Matoussi (2008), and when the two barriers are completely separated, we provide a complete wellposedness theory for doubly reflected second-order BSDEs. We also show that these objects are related to non-standard optimal stopping games, thus generalizing the connection between DRBSDEs and Dynkin games first proved by Cvitani? and Karatzas (1996). More precisely, we show under a technical assumption that the second order DRBSDEs provide solutions of what we call uncertain Dynkin games and that they also allow us to obtain super and subhedging prices for American game options (also called Israeli options) in financial markets with volatility uncertainty. 相似文献
6.
Ying Hu Gianmario Tessitore 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(5-6):825-846
In this paper, we study the existence and uniqueness of mild solutions to a possibly degenerate elliptic partial differential
equation in Hilbert spaces. Our aim is, in the case in which ψ(·, 0, 0) is bounded, to drop the assumptions on the size of λ needed in [11]. The main tool will be existence, uniqueness
and regular dependence on parameters of a bounded solution to a suitable backward stochastic differential equation with infinite
horizon. Finally we apply the result to study an optimal control problem.
相似文献
7.
We prove a general theorem that the -valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the -valued solutions for backward doubly stochastic differential equations on finite and infinite horizon with linear growth without assuming Lipschitz conditions, but under the monotonicity condition. Therefore the solution of finite horizon problem gives the solution of the initial value problem of the corresponding stochastic partial differential equations, and the solution of the infinite horizon problem gives the stationary solution of the SPDEs according to our general result. 相似文献
8.
This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs) with an unbounded terminal condition. Our results are deeply linked with a strong a priori estimate on Z that takes advantage of the Markovian framework. This estimate allows us to prove the existence of a viscosity solution to a semilinear parabolic partial differential equation with nonlinearity having quadratic or superquadratic growth in the gradient of the solution. This estimate also allows us to give explicit convergence rates for time approximation of quadratic or superquadratic Markovian BSDEs. 相似文献
9.
Feng Zhang 《Journal of Computational and Applied Mathematics》2010,233(8):1980-1986
In this paper we study one kind of coupled forward-backward stochastic differential equation. With some particular choice for the coefficients, if one of them satisfies a uniform growth condition and they are accordingly monotone, then we obtain the equivalence between the uniqueness of solution and its continuous dependence on x and ξ, where x is the initial value of the forward component and ξ is the terminal value of the backward component. 相似文献
10.
We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution are proved by a double penalization approach under regularity assumptions on the obstacle. In a suitable regime switching diffusion framework, we show the connection between our class of BSDEs and fully nonlinear variational inequalities. Our BSDE representation provides in particular a Feynman–Kac type formula for PDEs associated to general zero-sum stochastic differential controller-and-stopper games, where control affects both drift and diffusion term, and the diffusion coefficient can be degenerate. Moreover, we state a dual game formula of this BSDE minimal solution involving equivalent change of probability measures, and discount processes. This gives in particular a new representation for zero-sum stochastic differential controller-and-stopper games. 相似文献
11.
In this paper, on the basis of some recent works of Fan, Jiang and Jia, we establish a representation theorem in the space of processes for generators of BSDEs with continuous linear-growth generators, which generalizes the corresponding results in Fan (2006, 2007) [10] and [11] and Fan and Hu (2008) [9]. 相似文献
12.
In Briand and Hu (Probab Theory Relat Fields 136(4):604–618, 2006), the authors proved an existence result for BSDEs with
quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper
is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex
with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates
stated in Karoui et al. (Math Finance 7(1):1–71, 1997). With these tools in hands, we can derive the nonlinear Feynman–Kac
formula in this context. 相似文献
13.
This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal conditions. Using solely probabilistic arguments, we retrieve the existence and uniqueness result derived via PDE-based methods by Kobylanski (2000) [14]. This approach is related to the study of quadratic BSDEs presented by Tevzadze (2008) [19]. Our argumentation, as in Tevzadze (2008) [19], highly relies on the theory of BMO martingales which was used for the first time for BSDEs by Hu et al. (2005) [12]. However, we avoid in our method any fixed point argument and use Malliavin calculus to overcome the difficulty. Our new scheme of proof allows also to extend the class of quadratic BSDEs, for which there exists a unique solution: we incorporate delayed quadratic BSDEs, whose driver depends on the recent past of the Y component of the solution. When the delay vanishes, we verify that the solution of a delayed quadratic BSDE converges to the solution of the corresponding classical non-delayed quadratic BSDE. 相似文献
14.
Huijie Qiao 《Journal of Mathematical Analysis and Applications》2009,355(2):725-738
In this paper we study a class of infinite horizon backward stochastic differential equations (BSDEs) of the form
15.
Jinghai Shao 《Bulletin des Sciences Mathématiques》2006,130(8):720-738
Let (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton-Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux. 相似文献
16.
Thibaut Mastrolia 《Stochastic Processes and their Applications》2018,128(3):897-938
In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in particular cases. We apply these results to both the study of a gene expression model in biology and to the classical pricing problems in mathematical finance. 相似文献
17.
This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Itô representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a new dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. The main results are complemented by several interesting examples which illustrate their sharpness as well as important properties of the utility maximization BSDE. 相似文献
18.
Anthony Réveillac 《Statistics & probability letters》2012,82(1):151-157
In this note we consider a quadratic growth backward stochastic differential equation (BSDE) driven by a continuous martingale M. We prove (in Theorem 3.2) that if M is a strong Markov process and if the BSDE has the form (2.2) with regular data then the unique solution (Y,Z,N) of the BSDE is reduced to (Y,Z), i.e. the orthogonal martingale N is equal to zero, showing that in a Markovian setting the “usual” solution (Y,Z) (of a BSDE with regular data) has not to be completed by a strongly orthogonal component even if M does not enjoy the martingale representation property. 相似文献
19.
In the Brownian case, the links between dynamic risk measures and BSDEs have been widely studied. In this paper, we consider the case with jumps. We first study the properties of BSDEs driven by a Brownian motion and a Poisson random measure. In particular, we provide a comparison theorem under quite weak assumptions, extending that of Royer [21]. We then give some properties of dynamic risk measures induced by BSDEs with jumps. We provide a representation property of such dynamic risk measures in the convex case as well as some results on a robust optimization problem in the case of model ambiguity. 相似文献
20.
In this paper, we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equations (GRBSDEs in short) driven by a Lévy process, which involve the integral with respect to a continuous process by means of the Snell envelope, the penalization method and the fixed point theorem. In addition, we obtain the comparison theorem for the solutions of the GRBSDEs. As an application, we give a probabilistic formula for the viscosity solution of an obstacle problem for a class of partial differential-integral equations (PDIEs in short) with a nonlinear Neumann boundary condition. 相似文献