On Minimizing Risk in Incomplete Markets Option Pricing Models

Ola Hammarlid ()
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Ola Hammarlid: Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden

International Journal of Theoretical and Applied Finance (IJTAF), 1998, vol. 01, issue 02, 227-233

Abstract: I study the Bouchaud–Sornette, Schweizer and Schäl way of pricing options, presenting the methodology in accordance with Bouchaud–Sornette. The definitions of the wealth balance and risk from trading in options and stocks are presented. The problem of finding a risk minimizing strategy in an incomplete market model where a perfect hedge is not possible is analyzed. Using this strategy according to the approach of Bouchaud and Sornette the option is priced by a fair game condition. In this article I establish the equivalence between global and local risk minimization and prove an option price conjecture of Wolczyńska. I also investigate optimality for a stock portfolio with extra profit.

Date: 1998
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DOI: 10.1142/S0219024998000126

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