Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, BlackScholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent mar...

Let X be a Markov process characterized as the solution of a martingale problem with generator A, and let Y be a related observation process. The conditional distribution πt of X(t) given observations of Y up to time t satisfies certain martingale properties, and it is shown that any probability-measure-valued process with the appropriate martingale properties can be interpreted as the conditio...

Fast pricing of American-style options has been a difficult problem since it was first introduced to the financial markets in 1970s, especially when the underlying stocks’ prices follow some jump-diffusion processes. In this paper, we extend the “true martingale algorithm” proposed by Belomestny et al. (2009) for the pure-diffusion models to the jump-diffusion models, to fast compute true tight...

The present note addresses an open question concerning a sufficient characterization of the variance-optimal martingale measure. Denote by S the discounted price process of an asset and suppose that Q? is an equivalent martingale measure whose density is a multiple of 1− φ • ST for some S-integrable process φ. We show that Q? does not necessarily coincide with the variance-optimal martingale me...

We give a sufficient condition to identify the q-optimal signed and the q-optimal absolutely continuous martingale measures in exponential Lévy models. As a consequence we find that, in the onedimensional case, the q-optimal equivalent martingale measures may exist only, if the tails for upward jumps are extraordinarily light. Moreover, we derive convergence of the q-optimal signed, resp. absol...

The intent of these essays is to study the minimal entropy martingale measure, to examine some new martingale representation theorems and to discuss its related Kunita-Watanabe decompositions. Such problems arise in mathematical finance for an investor who is confronted with the issues of pricing and hedging in incomplete markets. We adopt the standpoint of a ra­ tional investor who principally...

The fact that the solution of a martingale problem for a diffusion process gives a weak solution of the corresponding Itô equation is well-known since the original work of Stroock and Varadhan. The result is typically proved by constructing the driving Brownian motion from the solution of the martingale problem and perhaps an auxiliary Brownian motion. This constructive approach is much more ch...