On dynamic programming equations for utility indifference pricing under delta constraints (Q534745)

The author considers a financial market with a finite time horizon, driven by an ordinary stochastic differential equation. On this market, he studies a problem of utility indifference pricing for a small investor under portfolio constrains for a HARA utility function defined over the positive real line. The optimal investment problem is solved using an associated dynamic programming equation. The utility indifference price of a European contingent claim with a discounted payoff \(F\) is then shown to satisfy \(q(x,F) = x + v(F:u_0(x))\), where \(u_0(x)\) is the maximal expected utility for inital wealth \(x\) and \(-v(\cdot:y)\) is a convex risk measure. The author shows that \(v\) is the value of an associated stochastic game and characterizes it as a viscosity solution to an associated dynamic programming equation.