Optimal inattention to the stock market with information costs and transactions costs

Information costs, which comprise costs of gathering and processing information about stock values and costs of deciding how to respond to this information, induce a consumer to remain inattentive to the stock market for finite intervals of time. Whether, and how much, a consumer transfers assets between accounts depends on the costs of undertaking such transactions. In general, optimal behavior by a consumer facing both information costs and transactions costs is state-dependent, with the timing of observations and the timing and size of transactions depending on the state. Surprisingly, if the fixed component of the transactions cost is sufficiently small, then eventually, with probability 1, a time-dependent rule emerges: the interval between observations is constant and on each observation date, the consumer converts enough assets to liquid assets to finance consumption until the next observation. If the fixed component of transactions costs is large, the optimal rule remains state-dependent indefinitely.