Melnikov, Alexander and Skornyakova, Victoria (2005) Efficient Hedging Methodology Applied to Equity-Linked Life Insurance. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
In this paper we study efficient hedging and its applications to the pricing of equitylinked life insurance contracts. We devote our attention to the pure endowment contracts with a flexible guarantee. In our setting, these insurance instruments are based on two risky assets of the market controlled by the Black-Scholes model during the contract period. The first asset is responsible for the maximal size of future profit while the second provides a flexible guarantee for the insured.
The insurance company is considered as a hedger of a maximum of two risky assets as a contingent claim in this market. The contract is exercised if the insured is still alive at the maturity time and cannot be perfectly hedged in view of a positive survival probability of a client. To provide an appropriate risk-management in connection of such a contract, the company should exploit some imperfect hedging forms. Here we propose the use of efficient hedging with a power loss function.
Specifying developments in this area, we create the pricing methodology for the insurance contracts under consideration in terms of a generalized Margrabe’s formula.
The results are illustrated by a numerical actuarial analysis with the indices Russell 2000
and Dow Jones Industrial Average.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Melnikov, Alexander and Skornyakova, Victoria|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 1/05|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||equity-linked life insurance, efficient hedging, flexible guarantee, pure endowment, Margrabe’s formula.|
|Deposited By:||DIANE MICHAUD|
|Deposited On:||02 Jun 2010 16:31|
|Last Modified:||08 Dec 2010 23:23|
AASE, K. and PERSSON, S. 1994. “Pricing of unit-linked insurance policies.” Scandinavian Actuarial Journal 1: 26-52.
BACINELLO, A.R. and ORTU, F. 1993. “Pricing of unit-linked life insurance with endogenous minimum guarantees.” Insurance: Math. and Economics 12:245-257.
BOWERS, N.L., GERBER, H.U., HICKMAN, J.C., JONES D.A. and
NESBITT, C.I. 1997. “Actuarial Mathematics.” Society of Actuaries, Schaumburg, Illinois.
BOYLE, P.P. and SCHWARTZ, E.S. 1977. “Equilibrium prices of guarantees under equity-linked contracts.” Journal of Risk and Insurance 44: 639-680.
BOYLE, P.P. and HARDY, M.R. 1997. “Reserving for maturity guarantees: Two approaches.” Insurance: Math. and Economics 21: 113-127.
BRENNAN, M.J. and SCHWARTZ, E.S. 1976. “The pricing of equity-linked life insurance policies with an asset value guarantee.” Journal of Financial Economics 3:195-213.
BRENNAN, M.J. and SCHWARTZ, E.S. 1979. “Alternative investment strategies for the issuers of equity-linked life insurance with an asset value guarantee.” Journal of Business 52: 63-93.
DELBAEN, F. 1986. “Equity-linked policies.” Bulletin Association Royale Actuaires Belges 80: 33-52.
FOELLMER, H. and LEUKERT, P. 2000. “Efficient hedging: cost versus short-fall risk.” Finance Stochast. 4: 117-146.
HARDY, M.R. 2003. “Investment guarantees: Modeling and risk-management for equity-linked life insurance.” J.Wiley.
MARGRABE, W. 1978. “The value of an option to exchange one asset to another.” J. of finance 33: 177-186.
MELNIKOV, A. 2004a. “Risk analysis in Finance and Insurance.” Chapman&Hall/CRC.
MELNIKOV, A. 2004b. “On efficient hedging of equity-linked life insurance policies.” Doklady Mathematics 69: 462-464.
MOELLER, T. 1998. “Risk-minimizing hedging strategies for unit-linked life-insurance contracts.” Astin Bulletin 28: 17-47.
MOELLER, T. 2002. “Hedging equity-linked life insurance contracts.” North American Actuarial Journal 5: 79-95.
SHIRYAEV, A.N. 1999. “Essentials of Stochastic Finance.” World Scientific.
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