The Role of Insurance in Investment Strategies

We consider an investment model with two sources of uncertainty. On the one hand, the company's future revenue depends on a random economic indicator, which follows a geometric Brownian motion. On the other hand, unexpected adverse events reduce a company's future revenue.  The times of occurrence of such events and their severity in the revenue reduction are both random. We model such events by means of a compound Poisson process.

The firm has to decide the moment to invest in the market and the insurance contract that it wants to buy. The decision of buying an insurance contract depends on the premium required and how the firm measures its risk. 

We formulate the model as a control problem that is solved using a dynamic programming approach.