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...

The main result of this paper is that a martingale evolution can be chosen for LIBOR such that, by appropriately fixing the drift, all LIBOR interest rates have a common market measure. LIBOR is described using a quantum field theory model, and a common measure is seen to emerge naturally for such models. To elaborate how the martingale for the LIBOR belongs to the general class of numeraires f...

In principle, liabilities combining both insurancial risks (e.g. mortality/longevity, crop yield,...) and pure financial risks cannot be priced neither by applying the usual actuarial principles of diversification, nor by arbitrage-free replication arguments. Still, it has been often proposed in the literature to combine these two approaches by suggesting to hedge a pure financial payoff comput...

Let X be the solution of a stochastic differential equation driven by a Wiener process and a compensated Poisson random measure, such that X is an L martingale. If H = Φ(Xs; 0 ≤ s ≤ T ) is in L, then H = α+ ∫ T 0 ξsdXs +NT , where N is an L martingale orthogonal to X (the Kunita-Watanabe decomposition). We give sufficient conditions on the functional Φ such that ξ has regular paths (that is, le...

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the value V B of the exponential utility ma...

In this paper, we consider a market with term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results direction: first, random field forward rates is driven by general semimartingale. Second, Heath–Jarrow–Morton (HJM) approach extended an additional component capturing those future jumps which are visible from current time. Third, associ...

In this paper, we present results on scalar risk measures in markets with transaction costs. Such are defined as the minimal capital requirements cash asset. First, some provided dual representation of such measures, particular emphasis given space variables (equivalent) martingale and prices consistent market model. Then, these representations used to obtain main paper time consistency for fri...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

The resource-bounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Speci cally, for any real number > 0, any uniformly polynomial-time computable sequence ~ = ( 0; 1; 2; : : : ) of real numbers (biases) i 2 [ ; 1 ], and any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positiv...