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A Markov process modeling and analysis of indifference pricing of insurance contracts for home reversion plan for a pair of insureds. (English) Zbl 1244.91077

The present article deals with the home reversion plan for a pair of retired houseowners in United Kingdom.
The home values follow a geometric Brownian motion and the insured are modeled by a multi-state continuous time Markov chain. Under an exponential utility function \[ u(w) = - \frac{1}{\alpha} e^{-\alpha w}, \quad \text{for some \(\alpha > 0\),} \] the authors derive systems of partial differential equations for the indifferent annuities and provide representations of their solutions in the following situations:
1) The insurance contract links the home reversion plan to long term care for a pair of insureds.
2) The home reversion plan for a pair of insureds is not linked to long term care.
The results are illustrated by numerical examples.

MSC:

91D20 Mathematical geography and demography
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J28 Applications of continuous-time Markov processes on discrete state spaces
60J65 Brownian motion
91B30 Risk theory, insurance (MSC2010)
49L20 Dynamic programming in optimal control and differential games
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