# Actuarial Value

Actuarial Value | |
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**Actuarial value** of a benefit or a premium in a traditional life insurance contract is the expected value of the revised benefit or premium (D. Schrager, A. Pelsser, 2004, pp. 369). In an UFK insurance policy, the history of mortality and pricing should be taken into account in calculating expected payment streams (D. Schrager, A. Pelsser, 2004 pp. 369). Therefore, the actuarial value of a stream of payments in an insurance policy is calculated as the conditional expected value of discounted payments, subject to the entire process history and determined by the following general formula (M. Schweizer, 2001, pp. 31).

Taking into account this filtration and thus the extended actuarial risk, the actuarial value of the end of the insurance period and the death benefit during the insurance period was determined as the basis for further net premium calculations (L. Ballotta, S. Habermann, 2006, pp. 195). Due to the fact that the financial risk is not subject to diversification, cash flows related to UFK insurance were valued for a homogeneous insurance portfolio. Actuarial value of the life insurance payment under the assumption of process independence mortality and the price process can be expressed as a general model (M. Schweizer, 2001, pp. 32-34).

Actuarial value of a benefit or a premium in a traditional life insurance contract is the expected value of the revised benefit or premium (D. Schrager, A. Pelsser, 2004, pp. 369). In an UFK insurance policy, the history of mortality and pricing should be taken into account in calculating expected payment streams (D. Schrager, A. Pelsser, 2004 pp. 369). Therefore, the actuarial value of a stream of payments in an insurance policy is calculated as the conditional expected value of discounted payments, subject to the entire process history and determined by the following general formula (M. Schweizer, 2001, pp. 31).

Taking into account this filtration and thus the extended actuarial risk, the actuarial value of the end of the insurance period and the death benefit during the insurance period was determined as the basis for further net premium calculations (L. Ballotta, S. Habermann, 2006, pp. 195). Due to the fact that the financial risk is not subject to diversification, cash flows related to UFK insurance were valued for a homogeneous insurance portfolio. Actuarial value of the life insurance payment under the assumption of process independence mortality and the price process can be expressed as a general model (M. Schweizer, 2001, pp. 32-34).

Actuarial value in the calculation of net premium for insurance UFK In classical life and annuity insurance, the net premium is determined based on the expected discounted value of future life insurance contracts (A. Bacinello, 2003, pp. 461). cash flows, i.e. their actuarial values. The basis for these calculations is the classical principle of equivalence, according to which the actuarial value of premiums and benefits resulting from the insurance agreement should be balanced over the entire insurance period. (A. Bacinello, 2003, pp. 461-487).

The net premium resulting from this principle is called fair and is determined in traditional insurance taking into account the risk-free rate and mortality risk. When an insurance company has a large portfolio, the risk of death is diversified according to the law of large numbers (A. Bacinello, 2003, pp. 461-487). In the case of UFK insurance, the insurer additionally bears the financial risk under the guarantee and there is no possibility of its diversification. It should be emphasized that most often UFK insurance policies are offered without a guaranteed sum, and thus the insurer does not take it into account in the calculations (M. Hardy, 2003, pp.273-275) . Therefore, the premium in UFK insurance should be determined taking into account the extended filtration generated by the insurance portfolio (in terms of mortality) and financial portfolio (in terms of price process) (M. Hardy, 2003, pp.273-275). Using the derived actuarial formulae and assuming t = 0, the one-off net UFK contribution according to the principle of equivalence is expressed as a general formula (M. Schweizer, 2001, pp. 37).

## Actuarial valuation

Actuarial valuation is a basic service provided by actuaries around the world. It involves assessing the risk and current value of financial projects (M. Hardy, 2003, pp. 275).
**It applies to both the insurance and reinsurance industries**. The actuary's task is to calculate the amount of future liabilities of the service recipient and prepare a plan to meet them without financial losses. Therefore, the task, as you can see, is a big challenge - the financial market never gives 100% guarantees (D. Schrager, A. Pelsser, 2004 pp. 372-373). However, an actuarial valuation conducted by a professional actuarial office with experience and qualifications (employing actuaries certified by the KNF) gives a very high probability of verifiability. Actuary is a specialist in insurance mathematics, as well as statistics and probability, economics, insurance accounting, as well as databases and mathematical modelling. This knowledge combined with modern and proven working methods allows for extremely accurate valuation (D. Schrager, A. Pelsser, 2004 pp. 372-373). The starting point for its implementation is the analysis of the initial situation of the company. In the case of actuarial valuation of employee reserves, issues such as the demographic structure of employees (gender, age, date of employment and working time), as well as their remuneration and financial position and issues such as employee turnover are taken into account (L. Ballotta, S. Habermann, 2006, p. 211). Based on these data, as well as information related to demographic and economic assumptions, such as the interest rate to discount future employee benefits, or the mortality and morbidity of employees in the future, a report is prepared presenting the valuation and guidelines for the conduct of subsequent years, in order to be able to maintain full profitability (L. Ballotta, S. Habermann, 2006, p. 211).

## Method of conducting actuarial valuation

Actuarial valuation is usually conducted using the individual prospective method - **this means that each time proven and individually adjusted tools are used**. International Accounting Standards (IAS 19) (L. Ballotta, S. Habermann, 2006, p. 212). Recommends the adoption of the projected unit benefit method, which assumes, first and foremost, a proportionate increase in the employer's obligation to pay non-salary benefits in the long term (L. Ballotta, S. Habermann, 2006, p. 212). The value of future obligations is treated by the actuary as part of the benefits, taking into account the expected salary, which is the basis on which they are calculated (A. Bacinello, 2003, pp.466-469).
Properly performed actuarial valuation and accuracy of its calculations is the best guarantee of its value in use for the ordering company. The forecast related, among others, to the age and personnel structure of the company will allow for precise forecasting of all liabilities due to severance payments, awards and not only and prepare for them in a reliable manner (A. Bacinello, 2003, pp. 466-469).

## References

- Anderson K., (2019).
*Accounting for Government Contracts--Cost Accounting Standards*, LexisNexis - Bacinello A., (2003).
*Fair Valuation of Guaranteed Life Insurance Participating Contact Embedding a Surrender Option*, "The Journal of Risk and Insurance", Vol.70, No. 3. pp. 461-487 - Ballotta L., Habermann S., (2006).
*The fair valuation problem of guaranteed annuity options: the stochastic mortality environment case*, Insurance Mathematics & Economics, vol. 38, pp. 195-214 - Carson J. M., Ostaszewski K.M, (2004).
*The Actuarial Value of Life Insurance Backdating*, Journal of Actuarial Practice, Vol. 11, pp. 64-66 - Code of Federal Regulations, (2012).
*Federal Acquisition Regulations System*, Code of Federal Regulations, Chapter 29 - Hardy M., (2003).
*Investment Guarantees. Modeling and Risk management for EquityLinked Life Insurance*John Wiley & Sons Inc. pp.273-275 - Ruppel W., (2012).
*Interpretation and Application of Generally Accepted Accounting Principles for State and Local Governments*, Wiley GAAP for Governments 2012, John Wiley & Sons - Schrager D., Pelsser A., (2004).
*Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance*, "Insurance Mathematics & Economics", vol 35, pp. 369-398 - Schweizer M., (2001).
*From actuarial to financial valuation principles*, "Insurance Mathematics and Economics 28(1)", pp. 31-47

**Author:** Bartosz Wojak