I am reading "Arbitrage Theory in Continuous Time" by Tomas Björk, and stumbled upon what seems to me an odd use of the superscript plus-symbol, so here it goes. One instance is found on page 11, given by:
$$(1^{\textbf{+}} R)x^{\textbf{+}} suy = \phi (u)$$.
The bold formatting on the plus symbol is slightly more aggressive in the book. The details aren't that important actually. But for the interested reader, as might seem obvious to some, this comes from the binomial model for pricing derivatives. R is the deterministic rate of interest (constant in fact), su is the stock value in good (up) times (as opposed to bad, sd, down), and y is stock holdings.
A bit out of context, the author also says that when the inequality $$ s(1+R) > su \Rightarrow s(1^{\textbf{+}}R)>sd$$ must also hold.
It might be obvious, but I am not sure how to interpret this use of the plus symbol. Can anyone help me?
Those are just bad printing, they are just regular addition.
It looks like they are saving $x$ amount in the bank and $y$ amount in the stock.
Hence $$(1+R)x + suy = \Phi(u)$$ $$(1+R)x+sdy=\Phi(d)$$
Equations $(2.2)$ and $(2.3)$ are obtained by solving for $x$ and $y$ using simultaneous linear equation.
The inequality that you stated is due to $u>d$.