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Chapter 7: Stochastic Differential Equations

mho1 Stochastic Processes and FInance Masters Englisch 18 Karten

Chapter 7: Stochastic Differential Equations

Karten in diesem Stapel (18)

  1. 1Stochastic differential equation (SDE)Stochastic differential equation (SDE)
  2. 2There is no reason why (in general) a solution to a SDE should exist. Even when they do exist they may not be unique.remark
  3. 3Lipschitz (function)Lipschitz (function)
  4. 4Criteria for existence and uniqueness of a solution to the SDE:Criteria for existence and uniqueness of a solution to the SDE:Criteria for existence and uniqueness of a solution to the SDE:
  5. 5Proposition: relationship of Lipschitz with continuous, differentiable, linear growth...Proposition: relationship of Lipschitz with continuous, differentiable, linear growth...
  6. 6Homogeneous SDEremove the time dependence in the first variable from f and g, i.e.Homogeneous SDE
  7. 7Brownian motion is the unique solution to the SDE....Brownian motion is the unique solution to the SDE....
  8. 8Brownian motion with drift is the unique solution to the SDE...Brownian motion with drift is the unique solution to the SDE...
  9. 9Stochastic Exponential of dM(t)=F(t)dB(t)+G(t)dtStochastic Exponential of dM(t)=F(t)dB(t)+G(t)dt
  10. 10The stochastic exponential of dM(t)=F(t)dB(t)+G(t)dt is the unique solution to the SDE...The stochastic exponential of dM(t)=F(t)dB(t)+G(t)dt is the unique solution to the SDE...
  11. 11Geometric Brownian MotionGeometric Brownian Motion
  12. 12geometric Brownian motion is the unique solution of the SDE...geometric Brownian motion is the unique solution of the SDE...
  13. 13The Ornstein-Uhlenbeck processThe Ornstein-Uhlenbeck process
  14. 14The Ornstein Uhlenbeck process is the unique solution to the SDE...The Ornstein Uhlenbeck process is the unique solution to the SDE...
  15. 15Linear SDE with additive noise has unique solution...Linear SDE with additive noise has unique solution...Linear SDE with additive noise has unique solution...
  16. 16diffusion processdiffusion process
  17. 17The solution to a homogeneous SDE is...The solution to a homogeneous SDE is...The solution to a homogeneous SDE is...
  18. 18If Y is the unique solution to (7.1.3), what is its associated pde? And what is the unique solution to the pde?If Y is the unique solution to (7.1.3), what is its associated pde? And what is the unique solution to the pde?If Y is the unique solution to (7.1.3), what is its associated pde? And what is the unique solution to the pde?

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Masters Stochastic Processes and FInance Karteikarten am Chapter 7: Stochastic Differential Equations, erstellt von mho1 am 07/06/2015.
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mho1
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