In this paper, we propose a pricing model for airbag options including discrete monitoring, time-varying barriers, early exercise opportunity, and other clauses simultaneously by a PDE approach. A closed-form solution is obtained in the classic Black-Scholes economy with no early exercise...

An investor receives utility bursts from realizing gains and losses at the individual-stock level (Barberis and Xiong, 2009, 2012; Ingersoll and Jin, 2013) and dynamically allocates his mental budget between risky and risk-free assets at the trading-account level. Using savings, he reduces his...