Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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COHERENT AND CONVEX HEDGING ON ORLICZ HEARTS IN INCOMPLETE MARKETS

  • Kim, Ju-Hong (Department of Mathematics, Sungshin Women's University)
  • 투고 : 2011.11.30
  • 심사 : 2012.03.06
  • 발행 : 2012.05.30
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초록

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

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과제정보

연구 과제 주관 기관 : Sungshin Women's University

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