The effects of technological shocks in an optimal goodwill model with a random product life cycle

We consider the optimal goodwill control problem in a segmented market where the length of the product life cycle is affected by unpredictable technological turbulence. In order to maximize profit over a random time horizon, a company controls the marketing efforts directed to each market segment. Assuming an exponential distribution for the product life cycle, we modify the optimal goodwill model into the infinite time horizon control problem. Based on the semigroup approach, we prove the existence and uniqueness of the optimal solution. We formulate optimality conditions for the problem and we prove the existence of a stationary long-run equilibrium. Next, we construct a numerical algorithm to find the optimal solution. Finally, we examine several scenarios of optimal marketing strategies.