小弟准备考金融工程(资产定价)博士,原来学经济学,窃以为实分析和泛函分析、常微分、偏微分、随机分析非常重要。
金融学中描述价格的波动是连续的但不可导,所以我们学的黎曼积分不行,必须用新的积分形式,所以实分析(测度论)和泛函分析非常重要。
推荐:《随机过程——金融资产定价之应用》,伍海华、杨德平,中国金融出版社
如果你想全面了解,
《微观金融学及其数学基础》,邵宇,清华大学出版社,很不错,是小百科全书
从国外流行的教材可以了解
Financial Mathematics and Probability References
Financial mathematics
M. Baxter, A. Rennie ``Financial Calculus. An Introduction to derivative pricing''
J. Cvitanic and F. Zapatero ``Introduction to the Economics and Mathematics of Financial Markets''
D. Duffie ``Security Markets. Stochastic models''
V. Goodman and J. Stampfli "The Mathematics of Finance: Modeling and Hedging"
J.C. Hull ``Options, Futures, and Other Derivatives''
I. Karatzas ``Lectures on the Mathematics of Finance''
I. Karatzas and S. Shreve "Methods of Mathematical Finance"
R. Korn and E. Korn ``Option Pricing and Portfolio Optimization''
D. Lamberton and B. Lapeyre ``Introduction to Stochastic Calculus Applied to Finance''
T. Mikosch ``Elementary Stochastic Calculus with Finance in View''
M. Musiela and M. Rutkowski ``Martingale Methods in Financial Modelling''
S.N. Neftci ``An Introduction to Mathematics of Financial Derivatives''
A.N. Shiriaev ``Essentials of Stochastic Finance : Facts, Models, Theory''
S. Shreve ``Stochastic Calculus for Finance'', vol I and II
P. Wilmott, S. Howison, J. Dewynne ``The Mathematics of Financial Derivatives. A Student Introduction''
D. Wong ``Generalised Optimal Stopping Problems and Financial Markets''
Undergraduate probability
Paul G. Hoel, Sidney C. Port and Charles J. Stone. ``Introduction to probability theory''
S. Karlin and H.M. Taylor ``A First Course in Stochastic Processes''
S. Karlin and H.M. Taylor ``A Second Course in Stochastic Processes''
Graduate probability
K.-L. Chung ``A course in probability theory''
R. Durrett ``Probability: theory and examples''
Stochastic analysis
R.F. Bass ``Probabilistic Techniques in Analysis''
K.L. Chung and R.J. Williams. ``Introduction to stochastic integration''
I. Karatzas and S.E. Shreve ``Brownian Motion and Stochastic Calculus''
T. Mikosch ``Elementary stochastic calculus with finance in view''
B. Øksendal ``Stochastic differential equations. An introduction with applications''
L.C.G. Rogers and D. Williams ``Diffusions, Markov Processes and Martingales, Vol. 2: Ito Calculus''
D. Williams ``Diffusions, Markov Processes and Martingales, Vol. 1: Foundations''