Optimal investment, consumption and timing of annuity purchase under a preference change

What Do We Know About Annuitization Decisions?

“…Risk aversion belongs to the factors that positively affect annuitization in most of the considered theoretical and empirical articles. The exceptions are Schulze and Post (2010) and Liang et al (2014), who show that the impact of risk aversion on annuity demand depends on other parameters, such as alternative investment volatility, and can be both positive and negative. Meanwhile, Bommier and Le Grand (2014) argue that the usual application of the linearly transformed utility function lacks the ability to explain low annuity demand.…”

“…(2015) find that negative stock returns can lead to additional purchases of variable annuities with guaranteed minimum withdrawal benefits (GMWBs) due to low fees and downside protection, and that the volatility of stock returns (underlying the variable annuity) generally negatively impacts demand (see also Steinorth and Mitchell, 2015, for ambiguous results). In contrast, Milevsky and Young (2007a) show, in their "anything anytime" model with full portfolio flexibility, that the volatility of investments serving as an alternative to annuities increases annuity demand (see also Hainaut and Devolder, 2006;Hwang et al, 2012;Liang et al, 2014). In addition, several authors examine the impact of different factors related to taxes and tax incentives on annuitization rates with varying results.…”

On the free boundary of an annuity purchase

“…The model in [7] is analogous to the one studied in [18], but with quadratic utility functions, and the authors find a closed-form solution: If (X t ) t≥0 represents the individual's wealth process, then it is optimal to stop when X leaves a specific interval (hence the optimal stopping boundary is formed by the endpoints of such an interval). In [11], in contrast to the previous papers, the authors assume that the individual may continue to invest and consume after annuitisation. By using martingale methods, explicit solutions are provided in the case of CRRA utility functions.…”

“…A constant force of mortality is also assumed in Gerrard et al [7] and Liang et al [11]. The model in [7] is analogous to the one studied in [18], but with quadratic utility functions, and the authors find a closed-form solution: If (X t ) t≥0 represents the individual's wealth process, then it is optimal to stop when X leaves a specific interval (hence the optimal stopping boundary is formed by the endpoints of such an interval).…”

“…By using martingale methods, explicit solutions are provided in the case of CRRA utility functions. Contrarily to [7], the optimal annuitisation in [11] occurs when the wealth process enters a specific interval, whose endpoints form the optimal stopping boundary.…”