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This paper discusses in detail the impact of shifts on the process variance ( σ 2 ) on the run length (RL) of modified upper one-sided EWMA charts for the process mean ( μ ) when the output is correlated. Quite apart from the relevance of a process variance change in its own right, a dilation in σ 2 can cause an undesirable stochastic decrease in the detection speed of some specific shifts in μ . This and other stochastic results are proved and illustrated with a few examples.

The neutral valuation approach for contingent claims in incomplete markets is based on the assumption that investors are identical utility maximizers and that derivative supply and demand are balanced. It is closely related to (marginal) utility-based pricing in the sense of Hugonnier et al. (2005), where however only buy-and-hold investments in the derivative are possible. This paper contains four results: Firstly, it is shown that neutral derivative prices exist in discrete-time markets with finite time horizon. They are characterized as martingales relative to certain finitely additive set functions. Secondly, it may happen that not any static utility-based derivative price can be extended to yield a neutral price process. Thirdly, neutral derivative prices may not exist in continuous-time markets. Finally, we consider the situation of finite utility on the whole real line.

We consider a multi-asset discrete-time model of a financial market with proportional transaction costs as described by Schachermayer [7]. In this model, the set of all self-financing trading strategies contains for example trading strategies which consist of buying an asset and selling it at the same time. In the presence of transaction costs this only generates a net loss of investor’s money. We introduce the notion of naive pure self-financing trading strategy. Agents using a naive pure self-financing trading strategy do not waste money the way described above. It is well known that the only strategies which do not generate a net loss of investor’s money due to transaction costs are the boundary points of the cone of portfolios available at price zero. We call these strategies pure self-financing trading strategies or just pure self-financing strategies. Next, we give a characterization of the set of pure self-financing strategies and of the set of naive pure self-financing strategies. Furthermore, we analyze the relationship between them. Finally, we establish a hedging theorem concerning these strategies.

The paper deals with the quickest detection of a change of the drift of the Brownian motion. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the optimal stopping problem for a diffusion Markov process. For this problem the optimal procedure is described and its characteristics are found. We show also that the same procedure is asymptotically optimal for the minimax formulation of the quickest detection problem.