Abstract: An Approach to the Greeks for Indifference Pricing
We consider the problem of the sensitivity of the indifference pricing to the dynamics of the underlying assets. In the context of arbitrage-free pricing (AFP), such sensitivities are known as the Greeks. Here, in multidimensional semimartingale settings of incomplete models, we develop the computations of the Greeks and the associated trading strategies for indifference pricing. Unlike the traditional AFP, e.g., in the Black-Scholes model, where the Greeks represent the sensitivity of a linear pricing problem to perturbations of the stock price dynamics, as indifference prices are given via solutions to (non-linear) optimization problems, their sensitivities to perturbations of model parameters, that is the Greeks, are also characterized by the value functions of (auxiliary quadratic) optimization problems, which we introduce too. We illustrate the results with positive examples.