On some expectation and derivative operators related to integral representations of random variables with respect to a PII process
نویسندگان
چکیده
Given a process with independent increments X (not necessarily a martingale) and a large class of square integrable r.v. H = f(XT ), f being the Fourier transform of a finite measure μ, we provide explicit Kunita-Watanabe and Föllmer-Schweizer decompositions. The representation is expressed by means of two significant maps: the expectation and derivative operators related to the characteristics of X . We also provide an explicit expression for the variance optimal error when hedging the claim H with underlying processX . Those questions are motivated by finding the solution of the celebrated problem of global and local quadratic risk minimization in mathematical finance.
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