Modern Tontine with Transaction Costs

TL;DR

This paper introduces a reversible modern tontine model with transaction costs, where retirees optimize wealth allocation and consumption through a stochastic control framework, revealing strategic transaction regions over time.

Contribution

It develops a novel stochastic and impulse control model for tontine management with transaction costs, characterizing the value function via a viscosity solution of a HJBQVI.

Findings

Identification of a V-shaped transaction region.

Dynamic adjustment of wealth in response to longevity credits.

Strategic rebalancing between tontine and bequest accounts.

Abstract

In this paper, we propose a new type of reversible modern tontine with transaction costs. The wealth of the retiree is divided into a bequest account and a tontine account. And consumption can only be withdrawn from the bequest account. Each transaction between the two accounts incurs fixed and proportional transaction costs depending on the transaction volume. The retiree dynamically controls the allocation policy between the two accounts and the consumption policy to maximize the consumption and bequest utilities. We formulate the optimization problem as a combined stochastic and impulse control problem with infinite time horizon, and characterize the value function as the unique viscosity solution of a HJBQVI (Hamilton-Jacobi-Bellmen quasi-variational inequality). The numerical results exhibit the V-shaped transaction region which consists of two stages. In the former stage, since longevity credits increase gradually, the retiree decreases the proportion of wealth in the tontine account to smooth the wealth and reduce the volatility. However, in the latter stage, the retiree increases the proportion of wealth in the tontine account to gamble for the considerable longevity credits.