In the first place the paper educes preparation theorem by the tool of martingale: no arbitrage equilibrium is the necessary condition of capital market efficiency.
Chapter 2 is the relative theory of stochastical analyse: including martingale, Brown Motion, Ito formula, Girsanov theorem, Markov process and Lipschitz condition etc.
In addition, some achievements on the theory domestic and adoard are presented. Chapter 1 presents some basic knowledge about asset valuation theory such as martingale about stochastic process, definition of Markov chains definition of ergodic, Jensen inequality, Marcinkiewicz strong law of large numbers the law of the iterated logarithm.
And then we discuss the basic knowledge and theory on the financial market by mathematical symbol and formula, such as Discrete- time models, Black-Scholes models and European contingent claim can be priced well by martingale method.
In the first place the paper educes preparation theorem by the tool of martingale: no arbitrage equilibrium is the necessary condition of capital market efficiency.
This paper proves that multiple default intensities are invariant under equivalent martingale transformation, given a well-diversified portfolio corresponding to the defaultable bond.
In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.