Sigma-martingale

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Lua error in package.lua at line 80: module 'strict' not found. In the mathematical theory of probability, a sigma-martingale is a semimartingale with an integral representation. Sigma-martingales were introduced by C.S. Chou and M. Emery in 1977 and 1978.[1] In financial mathematics, sigma-martingales appear in the fundamental theorem of asset pricing as an equivalent condition to no free lunch with vanishing risk (a no-arbitrage condition).[2]

Mathematical definition

An \mathbb{R}^d-valued stochastic process X = (X_t)_{t = 0}^T is a sigma-martingale if it is a semimartingale and there exists an \mathbb{R}^d-valued martingale M and an M-integrable predictable process \phi with values in \mathbb{R}_+ such that

X = \phi \cdot M. \,[1]

References

  1. 1.0 1.1 Lua error in package.lua at line 80: module 'strict' not found.
  2. Lua error in package.lua at line 80: module 'strict' not found.

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