This paper studies a contingent claim pricing problem in incomplete markets , based on the risk indifference principle . The seller's dynamic risk indifference price is the payment that makes the risk involved for the seller of a contract equal, at any time, to the risk involved if the contract is not sold and no payment is received. An explicit formula for the dynamic risk indifference price is given as the solution of a one-dimensional linear BSDE with stochastic Lipschitz coefficient . The results show that any convex risk measure used for indifference pricing leads to an equivalent martingale measure. This entails a simple linear representation of the price as the expected derivative payoff under the "risk indifference measure" . From a risk management perspective, the model provides two-sided risk indifference bounds for derivative prices in incomplete markets.
This paper studies a contingent claim pricing problem in markets where the underlying traded assets are illiquid. Based on the risk indifference principle , an explicit formula for the dynamic risk indifference price is given as the difference between the solutions of two one-dimensional BSDEs with stochastic Lipschitz coefficients . The results show that dynamic risk indifference prices provide tighter price bounds than dynamic upper and lower hedging prices. Besides, a linear version of the price is given as the marginal risk price, i.e., the risk indifference price of a vanishing amount of derivatives . From a risk management perspective, the model provides two-sided risk indifference bounds for derivative prices in incomplete markets.
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. The seller's dynamic risk indifference price is the payment that makes the risk involved for the seller of a contract equal, at any time, to the risk involved if the contract is not sold and no payment is received. An
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linear BSDE
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any convex risk measure used for indifference pricing leads to an equivalent martingale measure. This entails a simple linear representation
dynamic risk indifference prices provide tighter price bounds than dynamic upper and lower hedging prices. Besides, a linear version
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as the expected derivative payoff under the "risk indifference measure"
is given as the marginal risk price, i.e., the risk indifference price of a vanishing amount of derivatives