[econophile]

Here's a typical representation of reference dependent prefereces with loss aversion.

U(x) = g(x-R) if x >= R
U(x) = -L*g(R-x) if x < R

R is a reference point, g(.) is some function, and L is a parameter that corresponds to the degree of loss aversion.

Let's set up the problem of hedging. We have already bet $1,100 on the Steelers as a pk to win $1,000. We have the option of hedging any amount on the Dolpins at 1.962 to 1. To achieve a riskless outcome, we would wager $1,000/1.962 = 509.68 on the Dolphins. This guarantees a win of $491.32. This risk free win seems like a natural reference point. To compare a full hedge to smaller hedges, lets pick a simple form for our utility function, namely g(x) = x.

So our utility function is now
u(x) = x - 490.32 if x > = 490.32
u(x) = -L*(490.32 - x) if x < 490.32

There are two possible outcomes. If PITT wins, we win 1,000 minus H (the amount we bet on MIA). If MIA wins, we win 0.962*H.

So expected utility is
EU = .5*(1000 - H - 490.32) - .5*L*(490.32 - 0.962*H)

To find the optimal H, calculate
dEU/dH = (.481*L - .5)

if L > 1.039, then dEU/dH >0 and a 100% hedge is optimal.

You can try this out using other forms for g(x), but you will get similar answers for concave g(x).