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Appendix
Appendix
The force acting upon the net demand of an asset can also be formulated according to the neoclassical tradition. Investor i is assumed to buy securities when he expects this to be profitable, that is, when he expects that the rate of return at period Δit from buying k > 0 assets at price p(t) exceeds the interest returns to be obtained for the money. The rule for this decision is
On the left hand side are the expected monetary returns from the investment, and on the right hand side the interest returns for the invested money kp(t) at period Δit. We can transform the above inequality as
which quantity we defined as the ‚force acting upon the net demand of a risky asset‘ of a risk-neutral investor.
We get the above decision rule also in the case of an infinite investment horizon. Let time be divided in intervals Δit. Suppose investor i believes a constant change
in the asset price and a fixed interest rate r (1/Δit) throughout the future. The expected present value Bl ($) from investing in k > 0 securities during l time periods is then
Letting l → ∞, the infinite sum of this geometric series becomes
This investment is profitable, if the present value of expected revenues from the i...