lndifference pricing of a GLWB option in variable annuities

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      <subfield code="a">Choi, Jungmin</subfield>
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      <subfield code="a">lndifference pricing of a GLWB option in variable annuities</subfield>
      <subfield code="c">Jungmin Choi</subfield>
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      <subfield code="a">We investigate the valuation problem of variable annuities with guaranteed lifelong/lifetime withdrawal benefit (GLWB) options, which give the policyholder the right to withdraw a specified amount as long as he or she lives, regardless of the performance of the investment. We assume the static approach that the policyholder¿s withdrawal rate is a constant throughout the life of the contract. We apply the principle of equivalent utility to find the indifference price for a variable annuity with a GLWB contract with an equity-indexed death benefit. Using an exponential utility function, Hamilton-Jacobi-Bellman (HJB) type partial differential equations (PDEs) are derived for the pricing functions. We first assume the mortality is deterministic, and the pricing PDE is solved numerically using a finite difference method. The effects of various parameters are investigated, including the age at inception of the policyholder, withdrawal rate, risk-free rate, and volatility of the underlying asset. We also consider a roll-up option and analyze the effect of delaying the start of the withdrawals. Another pricing PDE is derived with a stochastic mortality, when the force of mortality is modeled with a stochastic differential equation. A finite difference method is used again to solve the pricing PDE numerically, and the sensitivities of the GLWB contracts with respect to the withdrawal rate and the risk-free rate are explored.</subfield>
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      <subfield code="a">Modelos actuariales</subfield>
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      <subfield code="t">North American actuarial journal</subfield>
      <subfield code="d">Schaumburg : Society of Actuaries, 1997-</subfield>
      <subfield code="x">1092-0277</subfield>
      <subfield code="g">05/06/2017 Tomo 21 Número 2 - 2017 , p. 281-296</subfield>
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