Abstract
Under the assumption that the time to death random variable follows a phase-type distribution, we study the pricing of two types of guaranteed minimum death benefit contracts: (i) GMDB with roll-up feature and (ii) GMDB with a fixed guarantee level. Within the Black-Scholes option pricing framework, we attempt to derive matrix-analytic formulas for the GMDB price and the total expenses. We also discuss an alternative Monte-Carlo method for practical applications.
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Ko, B., Bae, T. Pricing guaranteed minimum death benefit contracts under the phase-type law of mortality. Lobachevskii J Math 36, 198–207 (2015). https://doi.org/10.1134/S1995080215020109
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DOI: https://doi.org/10.1134/S1995080215020109