Pricing Bounds and Bang-bang Analysis of the Polaris Variable Annuities

We study the no-arbitrage pricing of Polaris variable annuities recently issued by AIG. Polaris allows the income base to “lock in” the high water mark of the investment account. For rider charge proportional to the... [ view full abstract ]

We study the no-arbitrage pricing of Polaris variable annuities recently issued by AIG. Polaris allows the income base to “lock in” the high water mark of the investment account. For rider charge proportional to the investment account, we establish a bang-bang solution for optimal withdrawal strategies and consequently design an innovative LSMC algorithm to efficiently obtain the optimal solution. The resulting value function is proved to be an upper bound of fair value for a contract with insurance fees charged on the income base and its super performance is confirmed by extensive numerical studies.