q here equals some appropriate r by the same logic as before. Here again, we usually read interpretations of (A2.8) which treat the appropriate r as an integral
of time preference or equivalently productivity rates over the interim (u,x).1
however see dV(x) as determined by current rate r(x) whether derived by present cost or present value methods. If the original investor remains the current owner, and now finds her time preference rate different, she will have factored asset modification costs into her original decision to bid or invest. If not, she will have traded to someone whose time preference rate is better suited. My counterparts to
(A2.1) and (A2.6) become
dV(x)=dPC(x)=F (uje dx and F (ujdu=dV(xjeTO™ (A2.9) and
V(x) =PC(x) = J Fewer du. (A2.10)
These equations seem the most straightforward reconciliation of the maximand rule, the convergence axioms and the evidence supporting risk theory. They describe individual assets over time, sometimes passing from one owner to another, rather than a given owner’s total portfolio. We maximize return within current risk tolerance, recognize that it will change, and deduct present value of expected
trading or asset modification costs from future value of flows while adding them to original value. This seems true to life. It allows discounting all expected positive flows over (x, z), and compounding all past negative ones over (0, x), at a single rate r(x) because of those adjustments to value or cost of flows. Tradition treats the
flows as fixed givens, and the discount rate as a function of interim time between x
and z or between 0 and x.
APPENDIX A: The Argument in Notation 3/7/16 7
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