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Mean-variance hedging for discontinuous semimartingales. (English) Zbl 1054.60051

Summary: Mean-variance hedging is well known as one of the hedging methods for incomplete markets. Our aim is to find a mean-variance hedging strategy for incomplete market models whose asset price process is given by a discontinuous semimartingale and whose mean-variance trade-off process is not deterministic. To this end, we focus on this problem under the following assumptions: (1) the local martingale part of the stock price process is a process with independent increments; (2) a certain condition restricting the number and the size of jumps of the asset price process is satisfied; (3) the mean-variance trade-off process is uniformly bounded; (4) the minimal martingale measure coincides with the variance-optimal martingale measure.

MSC:

60G48 Generalizations of martingales
91B28 Finance etc. (MSC2000)
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