A generalized pricing framework addressing correlated mortality and interest risks: a change of probability measure approach

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

“…But such attempts also started with the assumption of independence between the two rate processes. Only very recently that such a deficiency was addressed albeit at a gradual pace using some advanced mathematical techniques and only for cases of models with no-regime switching feature yet; see for example, Liu et al (2014).…”

“…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.…”

“…Under this model, which was employed as well in Liu et al (2014), the survival index S(t, T ) can be easily obtained as…”

“…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.…”

Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation

“…Even though extracting the Q-dependence might be more complicated, different papers investigated the valuation under dependent financial and actuarial risks (see e.g. Liu et al (2014), Deelstra et al (2016), Zhao and Mamon (2018)).…”