How Financial Mathematics and Risk Theory Differ
Summary
The document compares financial mathematics with risk theory and risk management, noting that their methods can overlap while their scope and probability conventions differ. Financial mathematics is presented as quantitatively focused, with applications such as pricing and portfolio management. Risk theory can also use quantitative models, but risk management may include qualitative concerns, such as operational risk.
A further distinction concerns probability measures. Financial mathematics may use either real-world probabilities or risk-neutral probabilities, depending on the modeling objective. Risk management is described as using the real-world measure. These are broad characterizations rather than strict boundaries: the discussion acknowledges methodological similarities and points to an additional reference, but does not develop a formal taxonomy or detailed examples.
Key ideas
- Financial mathematics is characterized as quantitatively oriented and includes pricing and portfolio management.
- Risk theory and risk management can include qualitative concerns alongside quantitative modeling.
- Financial mathematics may use real-world or risk-neutral probability measures depending on the objective.
- Risk management is described as relying on the real-world probability measure.
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Full text
# Risk theory is a part of financial mathematics # Risk theory is a part of financial mathematics 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. Please feel free to retag this question ## Answer by vonjd (score 4) https://quant.stackexchange.com/a/8389 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. ## Answer by SBF (score 2) https://quant.stackexchange.com/a/8390 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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