On dynamic programming equations for utility indifference pricing under delta constraints |
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Authors: | Takashi Adachi |
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Affiliation: | Fukushima Medical University, Fukushima City, Fukushima 960-1295, Japan |
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Abstract: | In this paper we study the problem of utility indifference pricing in a constrained financial market, using a utility function defined over the positive real line. We present a convex risk measure −v(•:y) satisfying q(x,F)=x+v(F:u0(x)), where u0(x) is the maximal expected utility of a small investor with the initial wealth x, and q(x,F) is a utility indifference buy price for a European contingent claim with a discounted payoff 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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Keywords: | Utility indifference price Portfolio constraint HARA utility Dynamic programming equation Viscosity solution |
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