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1.
In this paper, we examine the dependence of option prices in a general jump-diffusion model on the choice of martingale pricing measure. Since the model is incomplete, there are many equivalent martingale measures. Each of these measures corresponds to a choice for the market price of diffusion risk and the market price of jump risk. Our main result is to show that for convex payoffs, the option price is increasing in the jump-risk parameter. We apply this result to deduce general inequalities, comparing the prices of contingent claims under various martingale measures, which have been proposed in the literature as candidate pricing measures.

Our proofs are based on couplings of stochastic processes. If there is only one possible jump size then we are able to utilize a second coupling to extend our results to include stochastic jump intensities.  相似文献   

2.
We explain how the field of logarithmic‐exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential‐logarithmic series constructed in 9 , 6 , and 13 . On the other hand, we explain why no field of exponential‐logarithmic series embeds in the field of logarithmic‐exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non‐isomorphic models of Th$(mathbb {R}_{mbox{an, exp}})$; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.  相似文献   

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