How Actuarial Estimation and Quantitative Finance Complement Each Other

# On the interface between Quant finance and actuarial-science/insurance-math


# On the interface between Quant finance and actuarial-science/insurance-math












Actuaries (at least in Europe) are frequently severily lacking in quant finance topics. At best they are familiar with B&S model.

People going into quant finane or striving to become a quant on the other hand are often not aware that their knowledge could also be applied in an insurance context.

Classic quant-work-related topics are: options pricing, portfolio optimisation, credit risk. This topics are also ery relevant to insurers. The example below shows why. I will also add more examples later on.

Example (portfolio optimization) Consider a car insurer's portfolio. Such a portfolio consists of many individual contracts. Premium calculation is based on the equivalence principle. Premiums paid by the insured must at least cover the losses. Thus such a portfolio can generate positive or negative annual returns. Positive if premiums paid > losses, Negatative if premiums paid < losses. Also these returns change over time and are volatile. The portfolio also has a market value - even though the market is not nearly as liquid as the one for standard derivatives and the bid/ask spreads can be huge. Still, one can interpret one such portfolio as a stock with possible negative dividend.

A reinsurance company often holds fractions of such portfolios. Thus to optimize the potfolio structure they can apply portfolio-optimization theory. As far as I know there are even a couple of reinsurers out there that actually do that.

Literature: (some books and papers to showcase the interfacing of actuarial evaluation and derivatives pricing techniques)

- On Valuation and Risk Management at the Interface of Insurance and Finance (suggested in the comments)

- Pricing and Hedging Variable Annuities (because of the comprehensive list of references)

- ON THE RISK-NEUTRAL VALUATION OF LIFE INSURANCE CONTRACTS WITH NUMERICAL METHODS IN VIEW (application of monte carlo least squares to the pricing of early ecercise features inbedded in in life insurance contracts)

Questions:

- Literature suggestions on the application of option pricing, portfolio optimization etc. to insurance related topics

- Further examples as the one above

- What could quants working for banks/funds learn from actuaries ?

## Answer by lehalle (score 6)

https://quant.stackexchange.com/a/17711

Actuarial science traditionally focuses on estimation of joint probabilities using real data where math finance is on valuation of contracts under an arbitrary distribution.

It means the first one deals with methods of estimation of future distributions (the number of accidents of a given kind, the probability of someone with a given profile to have a specific disease, etc) using real data. The second one usually tries to answer to the valuation of a given payoff assuming the distribution is known. In the math finance vocabulary, the future of distributions is embedded into a filtration.

Note this is a narrow view of math finance, since it can be viewed as far more generic, but keep it simple here. If you read reference books like Essentials of Stochastic Finance: Facts, Models, Theory by Shiryaev, you can see it goes further than that.

Usually in insurance the contracts are not that sophisticated, and the difficult task is to obtain accurate estimations. Actuarial science is a collection of methods to build estimations on populations that are commonly useful for insurance contracts. It can be viewed as an applicative field of statistics.

When contracts are more sophisticated, of course the usual tools of the subset of math finance we are talking about are needed.

Math finance does not focus that much on distribution estimation for few reasons: the main one is for financial products signed by investment banks, the risk neutral measure is used (and it is perfectly known). Another is that math finance is about understanding the risk borne by the owner of a position (i.e. a contract).

Of course a good math finance quant can be useful for an insurance, especially now that capital requirements and solvency rules push pressure on such firms to understand a risk which components are market prices.

## Answer by Kiwiakos (score 3)

https://quant.stackexchange.com/a/17713

The classical connection is the http://en.m.wikipedia.org/wiki/Esscher_transform developed for actuaries in 1932 which essentially transforms the objective probability measure into the risk neutral one used in quant finance.

## Answer by Hartvigsen (score 1)

https://quant.stackexchange.com/a/17742

Option pricing theory and interest rate theory are used within life insurance mathematics. See for example the articles of Thomas Møller:

Local risk-minimization with survivor bonds (with L. Henriksen). To appear in Applied Stochastic Models in Business and Industry, 2014.

On systematic mortality risk and risk-minimization with survivor swaps (with M. Dahl and M. Melchior). Scandinavian Actuarial Journal 2008(2-3), 2008, 114-146.

Or

Hedging equity-linked life insurance contracts. North American Actuarial Journal 5(2), 2001, 79-95.