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Abstract
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We study indifference pricing of term annuities using exponential utility. Our model assumes both stochastic interest rates and stochastic hazard rate governing the mortality of all lives. We briefly review the continuous-time theory and summarize the results regarding the relevant HJB equation. We then focus on the discrete-time hazard rate model where more general cases can be considered. In particular, we derive a probabilistic simulation algorithm to price annuities for generic Markovian hazard rates. The algorithm is robust and avoids the difficulties of having to solve 2-dimensional nonlinear PDEs. It also allows to illustrate the theoretical conclusions with some concrete graphs and pictures. This is joint work with Jenny Young. |
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