A comonotonicity-based valuation method for guaranteed annuity options

Polynomial diffusion models for life insurance liabilities

“…Recent studies, see e.g. [35], [13] and [15], confirm the important role of this dependence structure when pricing life insurance liabilities.…”

Mortality modelling with regime-switching for the valuation of a guaranteed annuity option

“…These were first issued in 1839 recorded in the report of the Insurance Institute of London (1972) and gained much popularity in the 1970s through the 1980s in the UK. Recent research works on this area focus on developing efficient and accurate pricing and hedging approaches; see Haberman (2003, 2006), Chu and Kwok (2007), Liu et al (2013Liu et al ( , 2014, amongst others.…”

“…(22) and (24) will aid in the simplification of the GAO value under M2 and M3, respectively. This can be accomplished by using the change of measure technique pioneered in Geman et al (1995), and also utilised in the work of Liu et al (2013). In our case, we employ the concept of endowment-risk-adjusted measure by choosing the pure endowment price as the numéraire.…”

“…We then derive the endowment price under the assumption that the two factors are driven by independent Markov chains under each alternative modelling set-up. Consequently, we use the so-called endowment-riskadjusted measure, which was first introduced in Liu et al (2013) and show the significant benefits of the change of measure technique over Monte-Carlo-based implementation. In addition, we show the flexibility of RS models in accommodating a range of underlying states in our model framework by changing the states of each random factor.…”

“…This work constructs a new framework whereby the interest rate process follows a pure Markov RS model whilst the mortality rates are deemed to follow a regime-switching mortality model. The pricing, hedging and reserving problem for guaranteed annuity options (GAOs) were studied in Wilkie et al (2003) and Liu et al (2013Liu et al ( , 2014, amongst others. In this paper, we further propose two alternative RS mortality models motivated by the limitation of the RSGM, which does not provide analytical solution to the survival probability.…”