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

38 Pages Posted: 26 Nov 2019 Last revised: 29 Dec 2021

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 loss averse policyholder of a variable annuity with a guaranteed minimum maturity bene t. This financial guarantee is financed via a fee withdrawn directly from the investment account, which impacts the net investment return. A fair pricing constraint is defi ned in terms of the risk-neutral value of the final contract payout. We propose a new fee structure that adjusts to the investment mix maximizing policyholder's utility while keeping the contract fairly priced. 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. We assume that the policyholder's risk attitude is relative to a reference level, risk-seeking towards losses and risk-averse towards gains. 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: Actuarial mathematics; variable annuity; portfolio optimization; non-concave utility; stochastic control; loss aversion.

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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