This paper provides approximations to utility indifference prices  for a contingent claim in the large position size limit. Results are valid for general utility functions  and semi-martingale models. It is shown that as the position size approaches infinity, all utility functions with the same rate of decay for large negative wealths yield the same price. Practically, this means an investor should price like an exponential investor. In a sizeable class of diffusion models, the large position limit is seen to arise naturally in conjunction with the limit of a complete model and hence approximations are most appropriate in this setting .
Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative wealths is the primary driver of prices. For utilities with exponential decay, one may price like an exponential investor. For utilities with a power decay, one may price like a power investor after a suitable adjustment to the rate at which the position size becomes large. In a sizable class of diffusion models, limiting indifference prices are explicitly computed for an exponential investor. Furthermore, the large claim limit is seen to endogenously arise as the hedging error for the claim vanishes .
R
This paper provides approximations
Approximations
A
are provided
A
on the real line
R
all utility functions with the same rate of decay
the utility function's decay rate
R
yield the same price. Practically, this means an investor should
is the primary driver of prices. For utilities with exponential decay, one may
R
In a sizeable
For utilities with a power decay, one may price like a power investor after a suitable adjustment to the rate at which the position size becomes large. In a sizable
R
the large position
limiting indifference prices are explicitly computed for an exponential investor. Furthermore, the large claim
R
arise naturally in conjunction with the limit of a complete model and hence approximations are most appropriate in this setting
endogenously arise as the hedging error for the claim vanishes