• Title, Summary, Keyword: backward stochastic differential equation

Search Result 11, Processing Time 0.033 seconds

BACKWARD SELF-SIMILAR STOCHASTIC PROCESSES IN STOCHASTIC DIFFERENTIAL EQUATIONS

  • Oh, Jae-Pill
    • Korean Journal of Mathematics
    • /
    • v.6 no.2
    • /
    • pp.259-279
    • /
    • 1998
  • For the forward-backward semimartingale, we can define the backward semimartingale flow which is generated by the backward canonical stochastic differential equation. Therefore, we define the backward self-similar stochastic processes, and we study the backward self-similar stochastic flows through the canonical stochastic differential equations.

  • PDF

THE SOLUTIONS OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS

  • Han, Baoyan;Zhu, Bo
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.5_6
    • /
    • pp.1143-1155
    • /
    • 2011
  • In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.

MULTIDIMENSIONAL BSDES WITH UNIFORMLY CONTINUOUS GENERATORS AND GENERAL TIME INTERVALS

  • Fan, Shengjun;Wang, Yanbin;Xiao, Lishun
    • Bulletin of the Korean Mathematical Society
    • /
    • v.52 no.2
    • /
    • pp.483-504
    • /
    • 2015
  • This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in (y, z) non-uniformly with respect to t. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov's theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of [8] and [6] to the general time interval case.

REFLECTED BSDE DRIVEN BY A L$\acute{E}$VY PROCESS WITH STOCHASTIC LIPSCHITZ COEFFICIENT

  • Lu, Wen
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.5_6
    • /
    • pp.1305-1314
    • /
    • 2010
  • In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations driven by a Brownian motion and the martingales of Teugels associated with an independent L$\acute{e}$vy process having a stochastic Lipschitz coefficient. We derive the existence and uniqueness of solutions for these equations via Snell envelope and the fixed point theorem.

Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

  • Dong, Yongpeng;Fan, Shengjun
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.3
    • /
    • pp.985-999
    • /
    • 2018
  • This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

Lp-SOLUTIONS FOR REFLECTED BSDES WITH TIME DELAYED GENERATORS

  • Zhou, Qing
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.3
    • /
    • pp.793-819
    • /
    • 2016
  • In this paper, we establish the existence and uniqueness of the solution for a class of reflected backward stochastic differential equations with time delayed generator (RBSDEs with time delayed generator, in short) in the case when the terminal value and the obstacle process are $L^p$-integrable with p ${\in}$]1, 2[ for a sufficiently small Lipschitz constant of the generator and the time horizon T.

A FINANCIAL MARKET OF A STOCHASTIC DELAY EQUATION

  • Lee, Ki-Ahm;Lee, Kiseop;Park, Sang-Hyeon
    • Bulletin of the Korean Mathematical Society
    • /
    • v.56 no.5
    • /
    • pp.1129-1141
    • /
    • 2019
  • We propose a stochastic delay financial model which describes influences driven by historical events. The underlying is modeled by stochastic delay differential equation (SDDE), and the delay effect is modeled by a stopping time in coefficient functions. While this model makes good economical sense, it is difficult to mathematically deal with this. Therefore, we circumvent this model with similar delay effects but mathematically more tractable, which is by the backward time integration. We derive the option pricing equation and provide the option price and the perfect hedging portfolio.

Lp (p ≥ 1) SOLUTIONS OF MULTIDIMENSIONAL BSDES WITH TIME-VARYING QUASI-HÖLDER CONTINUITY GENERATORS IN GENERAL TIME INTERVALS

  • Lishun, Xiao;Shengjun, Fan
    • Communications of the Korean Mathematical Society
    • /
    • v.35 no.2
    • /
    • pp.667-684
    • /
    • 2020
  • The objective of this paper is solving multidimensional backward stochastic differential equations with general time intervals, in Lp (p ≥ 1) sense, where the generator g satisfies a time-varying Osgood condition in y, a time-varying quasi-Hölder continuity condition in z, and its ith component depends on the ith row of z. Our result strengthens some existing works even for the case of finite time intervals.

A Generalized Finite Difference Method for Solving Fokker-Planck-Kolmogorov Equations

  • Zhao, Li;Yun, Gun Jin
    • International Journal of Aeronautical and Space Sciences
    • /
    • v.18 no.4
    • /
    • pp.816-826
    • /
    • 2017
  • In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

OPTIMAL INVESTMENT FOR THE INSURER IN THE LEVY MARKET UNDER THE MEAN-VARIANCE CRITERION

  • Liu, Junfeng
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.3_4
    • /
    • pp.863-875
    • /
    • 2010
  • In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.