On dynamic programming equations for utility indifference pricing under transaction costs
摘要：
In this paper we study the problem of utility indifference pricing in the presence of proportional transaction costs, using a utility function defined over the positive real line. We present a convex risk measure -v(* : y) satisfying q(w, x, F ) = w + v(F + x : u(w : x)), where u(w :x) is the maximal expected utility of a small investor with initial holdings (w, x), and q(w, x, F ) is a utility indifference buy price for a European contingent claim F . We provide a dynamic programming equation associated with the risk measure (-v), and characterize v as a viscosity solution of this equation.
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