Secretarial Investment Models
F. Thomas Bruss and Thomas S. Ferguson
Abstract:
How should we invest capital into a sequence of investment opportunities, if,
for reasons of external competition, our interest focuses on trying to
invest in the very best opportunity? We introduce new models to answer such
questions. Our objective is to formulate them in a way that makes results
high-risk specific in order to present true alternatives to other models. At
the same time we try to keep them applicable in quite some generality, also
for different utility functions. Viewing high risk situations we assume that
an investment on the very best opportunity yields a lucrative, possibly
time-dependent, rate of return, that uninvested capital keeps its risk-free
value, whereas ``wrong'' investments lose their value. Several models are
presented, mainly for the so-called rank-based case. Optimal strategies and
values are found, also for different utility functions, and several examples
are explicitly solved. We also include results for the so-called full-information
case, where, in addition, the quality distribution of investment opportunities is
supposed to be known. In addition we present tractable models for an unknown
number of opportunities in terms of Pascal arrival processes. Effort is
made throghout the paper to justify assumptions in the view of applicability.