The document discusses mathematical reserve in the Greek insurance market. It defines mathematical reserve as the capital accumulated from premiums paid by the insured over the life of the insurance contract. Mathematical reserve increases over time as more premiums are paid in. It can be used as savings to provide lifelong pension payments to the insured or to cover costs like inheritance tax. Insurance companies in Greece calculate mathematical reserve using retrospective and prospective methods to determine future liabilities and payments in order to ensure sufficient funds are available.

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MATHEMATICAL RESERVE IN THE
GREEK INSURANCE MARKET: METHODS
OF CALCULATING
Σουλιώτης Λεωνίδας Σ11168
Supervisor: Νεκτάριος Μιλτιάδης

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TABLE OF CONTENTS
1) Introduction…………………………………………………..
2) Mathematical Reserveand Capital at Risk………………
3) Mathematical Reserveand Cash Surrender Value…...
4) Calculation of Mathematical Reserve……………………...
5) Exploitationof the Mathematical Reserve………………
6) Periodic Insurance Companies Examination(in the
U.S.A. InsuranceMarket)…………................................................
7) Conclusion.....................................................................................

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1) Introduction
“The foundation of life insurance is the recognition of the value of the
value of the human life and the possibility of indemnification for the
lost of that value.” A quote stated by O.C. Oviatt and defines perfectly
the meaning of Life Insurance. Life Insurance’s most common role is to
face the financial problems that occur after a sudden death. Without
Life insurance, it would be almost impossible for the family to save the
necessary capital in order to face the unexpected loss of income.
Furthermore, life-long Life Insurance is a great opportunity for
profitable investments. This investment occurs because of the high
premiums of the first years (in the ‘Level Premium Method’), which is
invested by the Insurance (according to the agreed Technical Interest)
Company in order to draw the premiums for the next years. This capital
is called Mathematical (or Legal) Reserve and it’s possession of the
insured person. It’s notable to declare that the Mathematical Reserve
it’s difficult to be accumulated when the premiums are paid by the
method of ‘Yearly Renewable term method’. Also, Mathematical
Reserve could be defined as the nominal value of the life insurance
contract when the insured person reaches the age of hundred (100)
years. A term that is not very useful to people who are not familiar with
economic terms and definitions.
12) Mathematical Reserve and Net Amount at Risk
Net amount at risk represents the net insurance part of the contract
that decreases as years go by. Simultaneously, the mathematical
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reserve is increasing. Thus, the compensations of death consist of two
parts:
 The mathematical reserve (Concerning the Savings)
 The net amount at risk (Concerning the Protection of insured
person)
The result is that the purpose of the mathematical reserve is to offer
lifelong protection. When an insured person reaches an advanced
amount of years, it would be affordable for him to pay the very high
premiums that would have been set by the insurance company. So,
mathematical reserve keeps the premiums in an affordable price and
the insured person could enjoy lifelong protection from the insurance.

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23) Mathematical Reserve and Cash Surrender Value
There are many cases that the insured people wants to cancel their Life
Insurance contracts and they ask a part or the whole premiums to be
returned to them. This action is called Cash Surrender and the capital
that is returned to the insured is called Cash Surrender Value. The Cash
Surrender, usually, is not accepted by the Insurance companies when
the insured people are still in life. When people think that their lives are
shaky and they are afraid of dying, in order not to lose the insured
capital, they ask for the Cash Surrender case. Usually, the Cash
Surrender Value equals the 80% percent or the ¾ of the Mathematical
Reserve, but that’s a general rule. In the Greek Insurance Market, there
is not a standard percent of the Mathematical Reserve that equals the
Cash Surrender Value. So, in theory, the upper limit of the Cash
Surrender Value is the whole Mathematical Reserve but in reality, the
Cash Surrender Value is fixed in a lower price. Necessary case for a
person to claim the Cash Surrender value is to have already pay the
premiums of the Insurance Contract for at least 3 years.
4) Calculation of Mathematical Reserve
The calculation of the Mathematical Reserve can be by using two
methods:
 The Retrospective Method (calculating deposits and payments in
the last period
 The Prospective method ( calculating the future deposits and
payments)
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Naturally, both ways generate the same result; the method cannot
change the result.
1. The Retrospective Method
The Mathematical Reserve equals the value of deposits that made till
that day reduced by the value of the payments made till that day.
Therefore, it is necessary to establish the current value of all deposits
and payments.
2. The Prospective Method
The calculation of the Mathematical Reserve can be made based on the
future deposits and payments. Namely, we will rely on the principle:
the Mathematical Reserve is supposed to cover all future liabilities
(payments) of the insurer. The total of all of those liabilities equals the
value of the future payments on the day the calculation is made,
reduced by the value of the future value of the future deposits on the
day the calculation is made. These values are gained by discounting of
the nominal values of the future payments and deposits.
5) Exploitation of the Mathematical Reserve
As it has already been stated, Mathematical Reserve is property of the
owner of the Insurance Contract. The must usual usage of this
accumulated capital is to be transformed into a lifelong pension annuity
(1). The Insurance Company could guarantee the payment of a pension
that would be higher than the capital that the insured would have
gathered if he saved money on its own, and also the Insurance

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Company could guarantee a lifelong payment. Furthermore, in some
countries, there is a regular practice that real estate should be passed
down from father to son. So, it would be difficult for some people to
pay the inheritance tax, and if they decide to do so,they have to sell a
part of their real estate. The result is that a Life Insurance contract is a sure
method for covering the costs of the inheritance tax (2). Last but not least,
most of the times, the accumulated capital is wasted by the beneficiaries of
the contract in ways that would not be approved by the owner of the
contract. This case can be minimized bysome special clauses that concern
the ways that the beneficiaries will take the accumulated capital(3).It has to
be noted that in the first case (1), the Mathematical reservewill be received
by the owner of the contract. Instead,in the case (2) and (3), the
accumulated capital will be received by the beneficiaries of the contract.
36) Periodic Insurance Companies Examination ( in the
U.S.A. Insurance Market)
Every year all legal reserve life insurance companies submit annual
statements to the insurance departmentsofeach state in which they are
licensed to do business.The format and contents of the forms used are
prescribed by the State Insurance Commissioners and theyare a detailed
report of an insurance company's financial status that is important in
evaluatingthe company's solvency and compliance with the insurance laws.
Every few years, dependingon a company's home state law, all companies
operatingin more than one state undergo a detailed home office zone
examinationofits financial position.This audit is conducted bya team of
State Insurance Department Examiners representingthe various zones in
which the companyis licensed to do business.Companieslicensed in only
3 Bill Johnston from http://abcja.sharepoint.com

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one state are subject onlyto an annual home office examination bytheir
State Insurance Department.
7) Conclusion
Mathematical Reserve plays an important role on every Life Insurance
contract. Moneyinvested by the Insurance Company as the contract is in
force. Because Mathematical Reserveis a result of a safe investment,more
people tend to sign a Life Insurance contract for beingprotected by the
inevitable case of death and for saving moneyfor the times theywon’t be
able to work or to ensure a capital forthe beneficiaries ofthe contract. The
next graph indicates the increase that the Mathematical reserveof the
‘Fortune Life’ Insurance Companyhas shown.

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Bibliography
1. Εισαγωγή στην Ιδιωτική Ασφάλιση, Νεκτάριος Μιλτιάδης,
Εκδόσεις Forum
2. Ασφαλίσεις Ζωής και Υγείας, Νεκτάριος Μιλτιάδης, Εκδόσεις
Σταμούλης
3.Εισαγωγή στην Ασφαλιστική Επιστήμη, Πέτρος Κιόχος, Εκδόσεις
Interbooks
4. Risk and Insurance, Mark R. Greene, South Western Publishing CO
5. http://abcja.sharepoint.com (Source from the Internet)
6. http://www.actaeconomica.efbl.org (Source from the Internet)