On the optimal use of put options under trade restrictions

Consider an agent who holds a stock, but is allowed to buy and hold some quantity of at-the-money put options on the stock. Such an agent must decide the optimal use of financial derivatives under trade restrictions. This paper uses simulation to compare the optimal quantity when the agent maximizes mean-variance utility or Value at Risk over wealth at option expiry. The optimal quantity is larger than the stock holding under mean-variance utility and precisely the same under value at risk. The options do not remove all variation in returns but still benefit the agent.