  We determine the optimal strategy for investing in a Black-Scholes market in
order to maximize the probability that wealth at death meets a bequest goal
$b$, a type of goal-seeking problem, as pioneered by Dubins and Savage (1965,
1976). The individual consumes at a constant rate $c$, so the level of wealth
required for risklessly meeting consumption equals $c/r$, in which $r$ is the
rate of return of the riskless asset.
  Our problem is related to, but different from, the goal-reaching problems of
Browne (1997). First, Browne (1997, Section 3.1) maximizes the probability that
wealth reaches $b < c/r$ before it reaches $a < b$. Browne's game ends when
wealth reaches $b$. By contrast, for the problem we consider, the game
continues until the individual dies or until wealth reaches 0; reaching $b$ and
then falling below it before death does not count.
  Second, Browne (1997, Section 4.2) maximizes the expected discounted reward
of reaching $b > c/r$ before wealth reaches $c/r$. If one interprets his
discount rate as a hazard rate, then our two problems are {\it mathematically}
equivalent for the special case for which $b > c/r$, with ruin level $c/r$.
However, we obtain different results because we set the ruin level at 0,
thereby allowing the game to continue when wealth falls below $c/r$.
