Indifference fee rate for variable annuities

Abstract

In this paper, we work on indifference valuation of variable annuities and give a computation method for indifference fees. We focus on the guaranteed minimum death benefits and the guaranteed minimum living benefits and allow the policyholder to make withdrawals. We assume that the fees are continuously payed and that the fee rate is fixed at the beginning of the contract. Following indifference pricing theory, we define indifference fee rate for the insurer as a solution of an equation involving two stochastic control problems. Relating these problems to backward stochastic differential equations with jumps, we provide a verification theorem and give the optimal strategies associated to our control problems. From these, we derive a computation method to get indifference fee rates. We conclude our work with numerical illustrations of indifference fees sensibilities with respect to parameters.

Insurance–finance arbitrage

“…This approach can be generalized to the quadratic hedging error. Finally, indifference pricing leads to a nonlinear pricing rule and we refer to Blanchet-Scalliet et al (2015), Chevalier et al (2016) for details and further literature. Nonlinear methods to analyze insurance contracts often use the axiomatic approach to risk measures on 𝐿 ∞ with the Fatou property and thus admitting robust presentations, see Tsanakas and Desli (2005); Barigou et al (2019); Engsner et al (2020) while this can also be treated on more general spaces, as for example, in Kaina and Rüschendorf (2009), Cheridito and Li (2009).…”

“…(2015), Chevalier et al. (2016) for details and further literature. Nonlinear methods to analyze insurance contracts often use the axiomatic approach to risk measures on $$L^\infty$$ with the Fatou property and thus admitting robust presentations, see Tsanakas and Desli (2005); Barigou et al.…”

No Arbitrage in Insurance and the QP-Rule

“…Fourth, indifference pricing leads to a non-linear pricing rule and we refer to Blanchet-Scalliet et al (2015), Chevalier et al (2016) for details and further literature. Finally, there are valuation methodologies utilizing risk measures, often based on an axiomatic view, see Tsanakas and Desli (2005), Pelsser and Stadje (2014), or on hedging, see Chen et al (2020).…”

A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives

“…Similarly, the solution y 0 needed to determine the value function V can be derived using a Euler scheme, see Chevalier et al (2014) for more details. In order to simulate the discretized BSDE above, we compute the conditional expectations involved using a the regression method in Gobet et al (2005) based on L 2 -projections on finite bases.…”