The minimal entropy martingale measure in a market of traded financial and actuarial risks

• Jan Dhaene ^[1] ; Ben Stassen ^[1] ; Pierre Devolder ^[2] ; Michel Vellekoop ^[3]
  1. [1] KU Leuven

     KU Leuven

     Arrondissement Leuven, Bélgica

     
  2. [2] Université Catholique de Louvain

     Université Catholique de Louvain

     Arrondissement de Nivelles, Bélgica

     
  3. [3] University of Amsterdam

     University of Amsterdam

     Países Bajos

     

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 282, Nº 1 (July 2015), 2015, págs. 111-133
• Idioma: inglés
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• Resumen

  • In arbitrage-free but incomplete markets, the equivalent martingale measure QQ for pricing traded assets is not uniquely determined. A possible approach when it comes to choosing a particular pricing measure is to consider the one that is ‘closest’ to the physical probability measure PP, where closeness is measured in terms of relative entropy.

    In this paper, we determine the minimal entropy martingale measure in a market where securities are traded with payoffs depending on two types of risks, which we will call financial and actuarial risks, respectively. In case only purely financial and purely actuarial securities are traded, we prove that financial and actuarial risks are independent under the physical measure if and only if these risks are independent under the entropy measure. Moreover, in such a market the entropy measure of the combined financial–actuarial world is the product measure of the entropy measures of the financial and the actuarial subworlds, respectively.