Department Seminar by Anne MacKay

Please Note: This seminar will be given online.

Fee structure and optimal investment mix in variable annuities

 In a complete market with bonds and equity, we study a portfolio optimization problem involving the rational policyholder of a variable annuity with maturity guarantee who aims to maximize the utility of her terminal wealth. This financial guarantee is financed via a fee withdrawn directly from the investment account, which impacts the net investment return. We propose a new fee structure that adjusts to the investment mix. A fair pricing constraint is defined in terms of the risk-neutral value of the final contract payout. We seek the investment strategy that maximizes the policyholder's expected utility of terminal wealth after the application of a financial guarantee and subject to the fair pricing constraint. This problem is formulated in terms of constrained optimal stochastic control and requires the maximization of a non-concave utility function. We solve the problem using a martingale approach and compare with existing results. Numerical results show that it is possible to find an optimal portfolio strategy for a wide range of fees, while keeping the contract fairly priced.