Indifference price with unbounded processes and claims: an Orlicz space approach

We consider a financial market where the discounted prices of the assets available for trading are modeled by a semimartingale that is not assumed to be locally bounded. In this case the appropriate class of admissible integrands is defined through a random variable W that controls the losses incurred in trading. In this general context, we study the utility maximization problem with an unbounded random endowment. By applying the theory of Orlicz spaces, this problem is stated and solved in a unified framework for both type of increasing concave utility functions: u:R->R and u:(0,infty)->R. We then apply the duality relation to compute the indifference price of a claim satisfying weak integrability conditions. For the exponential utility function, the indifference price leads to a convex risk measure whose dual representation is based on a set of singular functionals which belong to the dual space of an appropriate Orlicz space. The penalty term is split into an entropic component and a singular one that is interpreted as a measure of catastrophic events.

(*) The talk is based on joint works with S. Biagini and with S. Biagini, M. Grasselli, T. Hurd.

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning