Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees

29 Pages Posted: 26 Nov 2019 Last revised: 13 Jan 2020

See all articles by Anne MacKay

Anne MacKay

University of Quebec at Montreal (UQAM)

Adriana Ocejo

University of North Carolina at Charlotte

Date Written: November 8, 2019

Abstract

We study a portfolio optimization problem involving the rational policyholder of a variable annuity with a guaranteed minimum maturity benefit. This financial guarantee is fi nanced via a fee withdrawn directly from the investment account, which impacts the net investment return.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 de fined in terms of the risk-neutral value of the fi nal contract payout. We seek the investment strategy that maximizes the policyholder's expected utility of terminal wealth after the application of a fi nancial guarantee and subject to the fair pricing constraint. We solve the associated constrained stochastic control problem using a martingale approach and analyze the impact of the fee structure on the optimal investment strategies and payoff. Numerical results show that it is possible to nd an optimal portfolio for a wide range of fees, while keeping the contract fairly priced.

Keywords: Variable annuity, portfolio optimization, expected utility, optimal control, non-concave utility, guaranteed minimum maturity benefi t

JEL Classification: C61, G22

Suggested Citation

MacKay, Anne and Ocejo, Adriana, Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees (November 8, 2019). Available at SSRN: https://ssrn.com/abstract=3486858 or http://dx.doi.org/10.2139/ssrn.3486858

Anne MacKay

University of Quebec at Montreal (UQAM) ( email )

PB 8888 Station DownTown
Succursale Centre Ville
Montreal, Quebec H3C3P8
Canada

Adriana Ocejo (Contact Author)

University of North Carolina at Charlotte

9201 University City Blvd
Charlotte, NC 28223
United States

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