Trading with Safety Net

Abstract

In this talk, we study the case when the trader wants to be insured for the case of the loss resulting from his trading strategy. This is a typical situation which financial institutions (banks, investment funds, pension funds or hedging funds) face: they are implementing some trading strategy which include active trading in the stock and the money market. Since these institutions are in some extent responsible for the outcome of their trading, it is desirable that they would have only limited liability when the loss occurs. They can buy an option contract which would let them to keep the profits, but they would be forgiven the loss. Using the probability techniques combined with the techniques of the stochastic optimal control (Hamilton- Jacobi-Bellman equations), we can compute price of this product. Moreover, we can determine what is the optimal trading strategy for the holder of the contract and the hedging strategy for the seller of the contract. In many cases, the price of this type of insurance is surprisingly cheap.