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In my program on Financial mathematics we studied such topics as pricing, portfolio management, risk theory (probability of ruin of an insurance company) etc. However, now I often see a line between "financial mathematics" and "risk theory", with latter being also related to "actuarial science". I have a question thus, is there indeed such a distinction in the terminology, or that's just my impression, and if there is such a distinction in the terminology - why did it appear, that is what is the crucial difference between those concepts. Methods used are very similar - stochastic modeling and stochastic analysis.

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Whats the point? Some elements of the tools used in risk management are highly quantitative and definitely can be classified as part of financial mathematics, others not. I fail to see where this discussion is supposed to be going...unless of course you are a historian and look for a new book title for your upcoming treatise. –  Matt Wolf Jul 5 '13 at 16:25

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Financial mathematics (or Mathematical finance) is obviously clearly quantitatively oriented.

Risk theory can be quantitatively oriented but can also be broader in the sense of qualitative characteristics, see e.g. risk management or as an example for a more qualitatively oriented approach operational risk.

Another difference is that financial mathematics uses both real world and risk neutral probability measures (depending on what is the aim of the model, e.g. derivatives pricing or portfolio management) whereas risk management exclusively uses the real world measure.

See also this excellent article:
'P' Versus 'Q': Differences and Commonalities between the Two Areas of Quantitative Finance by Attilio Meucci.

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Even in the wikipedia article, they seem to consider both pricing and risk management as subsets of financial mathematics. The discussion on P and Q is indeed interesting, thanks for pointing it out. –  Ilya Jul 4 '13 at 11:46
Yes, but only the mathematical part of risk management but as I said risk management comprises also non-mathematical elements. –  vonjd Jul 4 '13 at 11:59
That I understand - I meant only the mathematical part. Anyways, say the problem of ruin probabilities will not classically fall into financial mathematics? –  Ilya Jul 4 '13 at 14:27
I would say that the mathematical part of risk management is also part of financial mathematics. –  vonjd Jul 4 '13 at 14:30

I have found a very nice discussion on the difference between the risk theory and the finance in Stochastic Processes in Insurance and Finance by P. Embrechts et al. - namely, section 4.1 discusses the methodological difference between the fields which I hope nicely adds to the answer of vonjd.

Although being short, I think it better fits the answer rather than a comment since it may be beneficial for other

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