We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors, making connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where for each n the claim h _n admits the decomposition h _n = D_n+Y_n where D_n is replicable and Y_n is completely unhedgeable in that the indifference price of Y_n for an exponential investor is its certainty equivalent. Under broad conditions, we may assume that Y_n vanishes in accordance with a large deviations principle as n grows. In this setting, we identify limiting indifference prices as the position size becomes large, and show the prices typically are not the unique arbitrage free price in the limiting market. Furthermore, we show that optimal purchase quantities occur at the large deviations scaling, and hence large positions endogenously arise in this setting.
We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors, making connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where for each n the claim B _n admits the decomposition B _n = D_n+Y_n where D_n is replicable and Y_n is completely unhedgeable in that the indifference price of Y_n for an exponential investor is its certainty equivalent. Under broad conditions, we may assume that Y_n vanishes in accordance with a large deviations principle as n grows. In this setting, we identify limiting indifference prices as the position size becomes large, and show the prices typically are not the unique arbitrage free price in the limiting market. Furthermore, we show that optimal purchase quantities occur at the large deviations scaling, and hence large positions endogenously arise in this setting.
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