Martingales and Financial Mathematics
Abstrak
In this expository paper, we will discuss the role played by martingales in Financial Mathematics. More precisely, we will restrict ourselves to a mathematical formulation of the economical concept of an arbitrage-free, complete market and the pricing of derivatives in such models. For a clear exposition, we only consider the discrete case. We also discuss the Cox-Ross-Rubinstein model which is still one of the most used models in Finance.
Referensi
Harrison, J.M. & Kreps, D.M., Martingales and Arbitrage in Multiperiod Securities Markets," J. of Economic Theory, 20, (1979), 381-408.
Harrison, J.M. & Pliska, S.R., Martingales and Stochastic Integrals in the Theory of Continuous Trading," Stochastic Processesand their Applications, 11, (1981), 215-260.
Koch Medina, P. & Merino, S., Mathematical Finance and Probability, BirkhÄ user, Basel, 2003.
Pliska, S.R., Introduction to Mathematical Finance, Blackwell, Oxford, 1997.
Veal, S.R., Stocks Bonds Options Futures, second edition, New York Institute of Finance, New York, 2001.
