### Actuarial Pricing vs Financial Mathematics Pricing

Posted:

**June 9th, 2011, 4:05 pm**Willmoter,is there any difference between actuarial pricing and pricing in the financial mathematics sense,i.e risk neutral ?

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Posted: **June 9th, 2011, 4:05 pm**

Willmoter,is there any difference between actuarial pricing and pricing in the financial mathematics sense,i.e risk neutral ?

Posted: **June 9th, 2011, 5:31 pm**

Different way of going about things, but should lead to same answers when asking the same questions. Actuarial is generally p(x,0)=E(x,t)*v(x,t) as opposed to (essentially) having building block prices based on derivatives with respect to time and an underlying. Actuarial methods are usually sloppier about including risk premium in interest rates, and in practice actuarial methods are generally used to produce prices based upon assumptions while financial mathematics tends to take prices as inputs.

Posted: **June 10th, 2011, 2:43 am**

I see,so pricing a contingent claim in both spheres gives the same price albeit ,the framework might be different .is there any interesting and active research in this area that is of Interest to both Insurance and Investment banks ?Cheers

Posted: **June 10th, 2011, 6:53 am**

The first thing that comes to mind where you might find a side by side comparison that might have some papers out about it is ILW pricing.

Posted: **June 10th, 2011, 11:57 am**

QuoteOriginally posted by: SamsaveelI see,so pricing a contingent claim in both spheres gives the same price albeit ,the framework might be different .is there any interesting and active research in this area that is of Interest to both Insurance and Investment banks ?CheersTake a look at catastrophe bonds.

Posted: **June 10th, 2011, 4:45 pm**

QuoteOriginally posted by: ehQuoteOriginally posted by: SamsaveelI see,so pricing a contingent claim in both spheres gives the same price albeit ,the framework might be different .is there any interesting and active research in this area that is of Interest to both Insurance and Investment banks ?CheersTake a look at catastrophe bonds.They are no longer priced using actuarial methods if ever.

Posted: **June 11th, 2011, 1:41 am**

QuoteOriginally posted by: HansiQuoteOriginally posted by: ehQuoteOriginally posted by: SamsaveelI see,so pricing a contingent claim in both spheres gives the same price albeit ,the framework might be different .is there any interesting and active research in this area that is of Interest to both Insurance and Investment banks ?CheersTake a look at catastrophe bonds.They are no longer priced using actuarial methods if ever.Are CAT bonds priced By Actuary's ? do Actuaries utilize intensive Numerical methods such as PDE,and FDM in modelling their pricing routines ?

Posted: **June 12th, 2011, 3:15 pm**

Here is a simple example: a stock price follows (real-world) GBM: dS = a S dt + sig S dW.The actuarial price of the option is the expected value, which obviously depends on (a,sig).If markets are perfect with constant interest rate r, the "financial math" price is the Black-Scholes value, which depends on (r,sig) but not a.In other setups, where the BS assumptions fail badly, you might want to proceed along the actuarial track, perhaps with an added discount factor.

Posted: **June 13th, 2011, 12:44 am**

QuoteOriginally posted by: SamsaveelAre CAT bonds priced By Actuary's ? do Actuaries utilize intensive Numerical methods such as PDE,and FDM in modelling their pricing routines ?Somewhat guessing, but I'm sure casualty insurance companies use actuarial pricing to decide if they should buy or sell at market prices. I don't think PDEs or FDMs would be used in the way you are probably thinking; in actuarial pricing, price is never thought to be a "real" thing that moves according to specific rules like drift and variance.

Posted: **June 13th, 2011, 9:53 am**

I think a good way to think about differences between actuarial pricing and financial mathematics is in terms of stochastic optimal control (or equivalently multistage stochastic optimisation). Large part of financial mathematics is solving a special kind of control problem - how to replicate/exceed a certain future payoff pattern under all possible scenarios by repeatedly trading a self financing portfolio. The control inputs here are trades carried out at each (small) time step. If the time evolution of the prices in the underlying assets is nice enough (essentially continuous) the fact that you have "controls" or "recourse"- i.e. the ability to adjust you actions based on what has just happened - effectively eliminates stochasticity and you get all the nice theory, closed form solutions etc.Actuarial pricing assumes that there are no "controls" available - you just get a sample drawn from some loss distribution - best you can do here is to aim for its expected value or some quantile.

Posted: **June 13th, 2011, 6:33 pm**

QuoteOriginally posted by: MarsdenDifferent way of going about things, but should lead to same answers when asking the same questions. Actuarial is generally p(x,0)=E(x,t)*v(x,t) as opposed to (essentially) having building block prices based on derivatives with respect to time and an underlying. Actuarial methods are usually sloppier about including risk premium in interest rates, and in practice actuarial methods are generally used to produce prices based upon assumptions while financial mathematics tends to take prices as inputs.Samsaveel, look at Marsden answer. Simply speaking the acturial way is to price assets and insurance policies as discounted cashflow and build some premium into. Thus it is mainly cash flow mapping subtracting costs. The current value of assets and liabilities were secondary as long as servicing insurance policies is working. However, in the near future all the other financial risks have to be considered in Solvency II (=a good demonstration that many rationals from the financial world are not working well for insurance supervisory = a big field experiment). the difference is that insurance firms need to value insurance policies (life, health, casualty) and banks financial contracts (loans, bonds, etc.) on their liability side. you rarely sell your insurance policies thus it is highly illiquid, long dated, or more like "real options". Risk are simply linked to the things you are insuring (actions and being of people, nature, etc.) and to lesser degree to market fluctations, bankcruptcy, funding risk or whatever (What happens if an insurance firm is closed? It will run off...).

Posted: **June 14th, 2011, 2:11 pm**

when Actuaries price a life insurance policy,there is the probability of death of the insured factor in the pricing equation,what is the analogue in the financial mathematics sense.if we proceed by pricing a life Insurance contract from a financial mathematics perspective do we still include the probability of death of the insured in the pricing equation to arrive at the expected PV ?

Posted: **June 15th, 2011, 11:34 am**

To paraphrase Oscar Wilde, financial mathematicians know the price of everything but the value of nothing. In FinMath, to a large degree, the market price is accepted as correct, and underlying probabilities are irrelevant. I don't think FinMath can really be used to set a price for an insurance contract just based on data. FinMath requires a market -- what is anyone willing to pay for the contract, and at what price is someone else willing to cover it?

Posted: **June 15th, 2011, 2:30 pm**

As both an actuary and a quant, I assure you that Financial and Actuarial Pricing are quite different.Financial Pricing is governed by no-arbitrage. If there is a "mispricing" it can be exploited to make free money so strong regularity between various asset prices is enforced. Insurance contracts, however, are illiquid, cannot generally be shorted, and price changes are regulated. "Mispricing" is routine and can persist indefinitely.Financial Pricing applies to "transferrable risk" while Actuarial Pricing applies to "retained risk". The truly interesting "problems" are contracts that contain both elements in an intertwined way. For example, the insurance industry routinely writes financial guarantees that say (in effect) "Thank you for holding our mutual fund. If you die, we will top off your mutual fund account so that your beneficiaries receive an amount equal to the highest quarter-end value ever attained in your mutual fund account." The market risk only exists if there is a death. Pricing this guarantee creates interesting problems.

Posted: **June 15th, 2011, 4:56 pm**

QuoteOriginally posted by: ClosetChartistAs both an actuary and a quant, I assure you that Financial and Actuarial Pricing are quite different.Financial Pricing is governed by no-arbitrage. If there is a "mispricing" it can be exploited to make free money so strong regularity between various asset prices is enforced. Insurance contracts, however, are illiquid, cannot generally be shorted, and price changes are regulated. "Mispricing" is routine and can persist indefinitely.Financial Pricing applies to "transferable risk" while Actuarial Pricing applies to "retained risk". The truly interesting "problems" are contracts that contain both elements in an intertwined way. For example, the insurance industry routinely writes financial guarantees that say (in effect) "Thank you for holding our mutual fund. If you die, we will top off your mutual fund account so that your beneficiaries receive an amount equal to the highest quarter-end value ever attained in your mutual fund account." The market risk only exists if there is a death. Pricing this guarantee creates interesting problems.any books on the subject of those guarantees and their pricing