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      A unified pricing of variable annuity guarantees under the optimal stochastic control framework

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          Abstract

          In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the existing numerical methods. For numerical valuation of these contracts, we develop a direct integration method based on Gauss-Hermite quadrature with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is very efficient when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We also present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a benchmark for practitioners and researchers developing pricing of variable annuity guarantees.

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          Most cited references29

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          Valuing American Options by Simulation: A Simple Least-Squares Approach

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            A cohort-based extension to the Lee–Carter model for mortality reduction factors

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              Financial valuation of guaranteed minimum withdrawal benefits

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                Author and article information

                Journal
                2016-05-01
                Article
                10.3390/risks4030022
                1605.00339
                72c8de5f-f70d-45f1-a8b3-c4fb66521c43

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Risks 2016, 4, 22
                Keywords: variable annuity, guaranteed living and death benefits, guaranteed minimum accumulation benefit, optimal stochastic control, direct integration method
                q-fin.PR

                Financial economics
                Financial economics

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