Optimal inventory and hedging decisions with CVaR consideration

We consider a newsvendor who makes an ordering decision to meet stochastic demand and buys a put option written on the demand to hedge against the risk of low demand to maximize his expected utility, which is measured by the conditional value-at-risk (CVaR). The put option is fairly priced with specifications for the strike price and the strike quantity. With the consideration of lost-sale penalty cost, we derive structural results on the optimal ordering and hedging polices. We show that the newsvendor will not order more than that without the option contract when the strike quantity is pre-determined and low, and he will order more when the strike quantity is a decision variable. Moreover, the optimal strike quantity is less than or equal to the optimal order quantity in the risk-neutral setting, and interestingly there are cases in which the optimal hedging ratio first increases, then keeps constant as the newsvendor becomes less risk averse. We also show that the value of the put option increases as the newsvendor becomes more risk averse and demand becomes more uncertain. Furthermore, the effect of risk aversion on the value of the option highly depends on the magnitudes of the system parameters.