  Mining blocks on a blockchain equipped with a proof of work consensus
protocol is well-known to be resource-consuming. A miner bears the operational
cost, mainly electricity consumption and IT gear, of mining, and is compensated
by a capital gain when a block is discovered. This paper aims at quantifying
the profitability of mining when the possible event of ruin is also considered.
This is done by formulating a tractable stochastic model and using tools from
applied probability and analysis, including the explicit solution of a certain
type of advanced functional differential equation. The expected profit at a
future time point is determined for the situation when the miner follows the
protocol as well as when he/she withholds blocks. The obtained explicit
expressions allow to analyze the sensitivity with respect to the different
model ingredients and to identify conditions under which selfish mining is a
strategic advantage.
