Mathematical finance is the branch of applied mathematics concerned with the financial markets.
The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive, and extend, the mathematical or numerical models suggested by financial economics. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock.
In terms of practice, mathematical finance also overlaps heavily with the fields of financial engineering and computational finance. Arguably, all three are largely synonymous, although the latter two focus on application, while the former focuses on modelling and derivation; see Quantitative analyst.
Many universities around the world now offer degree and research programs in mathematical finance.
Wednesday, April 4, 2007
Mathematical finance
Sunday, April 1, 2007
Mathematical economics
The term mathematical economics is employed in two main senses:
(1) As a specialized area of study, mathematical economics is a distinct sub-field within the discipline of economics concerned with the application and development of mathematical techniques to shed light on economic problems. Paul Samuelson's Foundations of Economic Analysis (1947) is considered a classic statement of contemporary mathematical economics.
(2) As a general set of analytical methods, mathematical economics—or, to distinguish it from the first sense employed above, the mathematical method of economics—represents a widely though by no means universally adopted approach to the presentation and interpretation of economic problems.
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While the field of mathematical economics is widely acclaimed (due in large part to the success of its progeny, mathematical finance), the widespread use of mathematical methods in economics is controversial. Opponents of the mathematical method, notably the Austrian School, argue that the use of formal techniques lends to the field an impression of scientific exactness that, by nature of the eccentricities of its human subject matter, is unfeasible, even in principle. By contrast, proponents argue that the validity of the mathematical method derives from economists' distinctive assumptions about the internal mechanics of economic decision-making: economic agents are generally (and, to many social scientists, strangely) assumed to be (i) rational and (ii) self-interested, from which it follows that an economic agent's deductions and behaviour may be compared against the calculations reached using formal logical and analytical techniques, including optimization and other advanced mathematical procedures. The rational-actor framework has been disputed as a valid characterization of human decision-making, but it remains the primary framework in mainstream economics.
Although the mathematical method of economics has evolved through geometric, algebraic and higher forms, a solid grasp of modern algebraic methods is a prerequisite for formal study, not only in mathematical economics, but in economics generally. For instance, the Journal of Economic Theory, one of the most prominent academic references in the field, is the apotheosis of the mathematical approach—though surprisingly, according to the Editors, it is a non-specialist journal.
From Wikipedia, the free encyclopedia
