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...ure is given by Λ(T ) = exp (∫ T 0 hr(u)dW r(u) − 1 2 ∫ T 0 (hr(u))2du ) , where hr is defined by (4.6). In general, the variance optimal martingale measure P and the minimal martingale measure P differ. However, we find below that they coincide in our model. Since hr(t) is G(t)-measurable, the density Λ(T ) is G(T )-measurable, and therefore it can be represented by a constant D and a stochastic integral with respect to P ∗(·, T ), see e.g. Pham, Rheinlander and Schweizer (1998, Section 4.3). Thus, we have the following representation of Λ(T ) Λ(T ) = D + ∫ T 0 ζ(u)dP ∗(u, T ). (8.8) Schweizer (1996, Lemma 1) gives that Λ(T ) is the density for the variance optimal martingale measure as well, i.e. dP dP = Λ(T ), such that P = P . Hence, under the equivalent martingale measure P , the dynamics of the mortality intensity and the intensity of the counting process N(x) are unaltered. For later use, we introduce the P -martingale Λ(t) := EP [Λ(T )|F(t)] = EP [Λ(T )|G(t)]. Note that Λ(T ) = Λ(T ). If hr is constant, calculations similar to those in Møller (2003b) for the Black-Scholes case give that Λ(t) Λ(t) = e−(h r)2(T−t). 8.3 Mean-variance indifference pricing for pure endo...

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... with market factors modelled as a diffusion process (rather than as a Markov chain). Along another line, the mean-variance hedging problem was investigated by Duffie and Richardson [6] and Schweizer =-=[22]-=-, where an optimal dynamic strategy was sought to hedge contingent claims in an imperfect market. Optimal hedging policies [6], [22] were obtained primarily based on the so-called projection theorem. ...

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...ter typically is done according to some optimality criterion involving the original probability measure. Examples are the minimal martingale measure [FSchw91], the variance optimal martingale measure =-=[Schw96]-=- or the minimal entropy martingale measure [Ft00]. We note that choosing a particular pricing measure determines a valuation for the claim but does not settle the hedging problem – unless the pricing ...

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... way one gets several well established martingale measures like the minimal martingale, the q-optimal measure, the 1sminimal entropy measure, the Esscher–measure, or the variance minimal measure (see =-=[37, 6, 29, 4, 11, 13]-=-). A second general approach is the utility based indifference price and variants of it due to [21] and [5] (see also [28]). The utility indifference price is in one to one correspondence with the mar...