论文标题
现代丁丁与交易成本
Modern Tontine with Transaction Costs
论文作者
论文摘要
在本文中，我们提出了一种具有交易成本的新型可逆现代丁丁。退休人员的财富分为遗产帐户和丁丁帐户。并且只能从遗产帐户中撤回消费。两个帐户之间的每笔交易都会根据交易量产生固定和比例交易成本。退休人员动态控制两个帐户和消费策略之间的分配策略，以最大程度地利用消费和遗赠实用程序。我们将优化问题作为随机和冲动控制问题与无限时间范围的结合，并将值函数表征为HJBQVI（Hamilton-Jacobi-Bellmen quasi-bellmen quasi-variatiatiation不平等）的唯一粘度解决方案）。数值结果表现出由两个阶段组成的V形交易区域。在前一阶段，由于长寿信用逐渐增加，退休人员会减少丁托丁帐户中财富的比例，以使财富平滑并降低波动。但是，在后期，退休人员增加了丁丁帐户中财富的比例，以赌博寿命。
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 And consumption can only be withdrawn from the bequest account.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.
