An Optimal Stochastic Control Framework for Determining the

نویسندگان

  • Peter Forsyth
  • Kenneth Vetzal
چکیده

5 An implicit partial differential equation (PDE) method is used to determine the cost of hedg6 ing for a Guaranteed Lifelong Withdrawal Benefit (GLWB) variable annuity contract. In the 7 basic setting, the underlying risky asset is assumed to evolve according to geometric Brownian 8 motion, but this is generalized to the case of a Markov regime switching process. A similarity 9 transformation is used to reduce a pricing problem with K regimes to the solution of K cou10 pled one dimensional PDEs, resulting in a considerable gain in computational efficiency. The 11 methodology developed is flexible in the sense that it can calculate the cost of hedging for a va12 riety of different withdrawal strategies by investors. Cases considered here include both optimal 13 withdrawal strategies (i.e. strategies which generate the highest possible cost of hedging for the 14 insurer) and sub-optimal withdrawal strategies in which the policy holder’s decisions depend on 15 the moneyness of the embedded options. Numerical results are presented which demonstrate 16 the sensitivity of the cost of hedging (given the withdrawal specification) to various economic 17 and contractual assumptions. 18

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تاریخ انتشار 2014