Common Notation for General Equilibrium with Asset Markets


T = set of time periods (usually, t = 0 is present; t = 1, 2, .. is future, t = T is doomsday).
S = set of states (#S = S)
H = set of households (#H = H)
F = set of financial assets (#F = F)
K = set of firms (#K = K)
n = number of physically differentiated goods.
pis = spot price of good i in state s.
ps = spot prices in state s
p = [p0, p1, .., pS] = vector of spot prices.


BA = Arrow-Debreu budget set.
xish = amount of commodity i received by household h H in state s S.
xsh = vector of commodities assigned to household h H in state s S.
xh = [x0h, x1h, x2h, .., xSh] = consumption plan of household h H.
uh: Rn(S+1) R - utility function of household h.
y h: Rn(s+1) R R - indirect uility function of household h.
p sh: probability of state s as believed by household h.
eh = [e0h, e1h, e2h, .., eSh] = endowment pattern of household h H.
l sh = Lagrangian multiplier of sth constraint of household h's optimization problem

BR = Radner budget set.
m sh = marginal valuation of state s by household h, m sh = p sh( ush/ xsh) = (p sh/l 0h)( y sh/ msh)
m h = [1, m 1h, m 2h, .., m Sh] = vector of state prices.
m h-0 = [m 1h, m 2h, .., m Sh] = vector of state prices minus the first argument.
t sh = net transfer of purchasing power to/from state s S+1 by household h.
W = hyperplane denoting asset market constraint.
W^ = hyperplane perpindicular to W.


afh = amount of asset f F purchased by household h.
ah = [a1h, a2h, .., aFh] = portfolio purchased by household h
qf = price of asset f F.
r fs = payoff of asset f in state s.
rfs = monetary return of asset f in state s, rfs = psr fs
Rfs = financial return of asset f in state s, Rfs = rfs/qf
r = risk-free return on a bond.
rf: S R = [rf1, rf2, .., rfS] = random variable denoting returns of asset f F (also denoted Vf)
rs: F R = [r1s, r2s, .., rFs] = distribution of returns across assets in state s S (also denoted Vs)
V = S F matrix of returns with rf, f = 1, .., F in columns and rs, s = 1, .., S as rows.


Yk = production set of firm k K.
yk = [y0k, y1k, .., ySk] = production plan of firm k.
Tk(yk) = transformation function of firm k.
vk = market value of firm k
d sk = dividend paid by firm k in state s.
bk = portfolio purchased by firm k (= negative of debt issued by firm k).
q hk = percentage of firm k owned by household h.