This book presents papers on continuous-time consumption- investment
models by Suresh Sethi and various co-authors. Sir Isaac Newton said
that he saw so far because he stood on the shoulders of gi- ants. Giants
upon whose shoulders Professor Sethi and colleagues stand are Robert
Merton, particularly Merton's (1969, 1971, 1973) seminal papers, and
Paul Samuelson, particularly Samuelson (1969). Karatzas, Lehoczky, Sethi
and Shreve (1986), henceforth KLSS, re- produced here as Chapter 2,
reexamine the model proposed by Mer- ton. KLSS use methods of modern
mathematical analysis, taking care to prove the existence of integrals,
check the existence and (where appro- priate) the uniqueness of
solutions to equations, etc. KLSS find that un- der some conditions
Merton's solution is correct; under others, it is not. In particular,
Merton's solution for aHARA utility-of-consumption is correct for some
parameter values and not for others. The problem with Merton's solution
is that it sometimes violates the constraints against negative wealth
and negative consumption stated in Merton (1969) and presumably
applicable in Merton (1971 and 1973). This not only affects the solution
at the zero-wealth, zero-consumption boundaries, but else- where as
well. Problems with Merton's solution are analyzed in Sethi and Taksar
(1992), reproduced here as Chapter 3.
