In an incomplete financial market in which the dynamics of the asset prices is driven by a d-dimensional continuous semimartingale X, we consider the problem of pricing European contingent claims embedded in a power utility framework. This problem reduces to identifying the p-optimal martingale measure, which can be given in terms of the solution to a semimartingale backward equation. We use th...

We introduce the partial martingale difference correlation, a scalar-valued measure of conditional mean dependence of Y given X, adjusting for the nonlinear dependence on Z, where X, Y and Z are random vectors of arbitrary dimensions. At the population level, partial martingale difference correlation is a natural extension of partial distance correlation developed recently by Székely and Rizzo ...

The Esscher transform is one of the very useful methods to obtain the reasonable equivalent martingale measures, and it is defined with relation to the corresponding risk process. In this article we consider two kinds of risk processes (compound return process and simple return process). Then we obtain two kinds of Esscher transformed martingale measures. The first one is the one which was intr...

We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.

In this paper we give a characterization of minimal distance martingale measures with respect to f-divergence distances in a general semimartin-gale market model. We provide necessary and suucient conditions for minimal distance martingale measures and determine them explicitly for exponential L evy processes with respect to several classical distances. It is shown that the minimal distance mar...

Inference for the mean difference in the two-sample random censorship model is an important problem in comparative survival and reliability test studies. This paper develops an adjusted empirical likelihood inference and a martingale-based bootstrap inference for the mean difference. A nonparametric version of Wilks' theorem for the adjusted empirical likelihood is derived, and the correspondin...

It is often documented, based on autocorrelation, variance ratio and power spectrum, that exchange rates approximately follow a martingale process. Because autocorrelation, variance ratio and spectrum check serial uncorrelatedness rather than martingale difference, they may deliver misleading conclusions in favor of the martingale hypothesis when the test statistics are insigniÞcant. In this pa...

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in [3, 24]. Further, by suitable adaptation of the notion of cyclical monotonicity, [4] obtained an extension of the one-dimensional Brenier’s theorem to the present martingale version. In this paper, we complement the previou...

In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, p-optimal martingale measures, bilateral Esscher transforms and the minimal martingale measure. We illustrate our theory by a n...