Indifference price

In finance, indifference pricing is a method of pricing financial securities with regard to a utility function. The indifference price is also known as the reservation price or private valuation. In particular, the indifference price is the price at which an agent would have the same expected utility level by exercising a financial transaction as by not doing so (with optimal trading otherwise). Typically the indifference price is a pricing range (a bid-ask spread) for a specific agent; this price range is an example of good-deal bounds.

Given a utility function ${\displaystyle u}$ and a claim ${\displaystyle C_{T}}$ with known payoffs at some terminal time ${\displaystyle T}$. If we let the function ${\displaystyle V:\mathbb {R} \times \mathbb {R} \to \mathbb {R} }$ be defined by

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