This paper focuses on two main issues that are based on two important concepts: exponential Levy process and minimal entropy martingale measure. First, we intend to obtain   risk measurement such as value-at-risk (VaR) and conditional value-at-risk (CvaR) using Monte-Carlo methodunder minimal entropy martingale measure (MEMM) for exponential Levy process. This Martingale measure is used for the...

We discuss martingale transforms between Hardy-amalgam spaces H p , q s Q and id="M2"> mathvariant="script">P . Let id="M3"> 0 < ∞ 1 id="M4"> let id="M5...

The equivalent martingale measures for the geometric Lévy processes are investigated. They are separated to two groups. One is the group of martingale measures which are obtained by Esscher transform. The other one is such group that are obtained as the minimal distance martingale measures. We try to obtain the explicit forms of the martingale measures, and we compare the properties of the mart...

This paper is about Polya’s Urn and the Martingale Convergence Theorem. I will start with the formal definition, followed by a simple example of martingale and the basic properties of martingale. Then I will explain the Polya’s Urn model and how it contributes to proving the Martingale Convergence Theorem. Finally, I will give a full proof of the Martingale Convergence Theorem.

1 Processus stochastiques, rappels 2 1.1 Espérance conditionnelle . . . . . . . . . . . . . . . . . . . . . 2 1.2 Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Processus de Markov . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Mouvement brownien, processus de Poisson (rappels) 4 1.3.2 Générateur . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.3 Martingal...

We consider a dynamic reinsurance market, where the traded risk process is driven by a jump-diffusion and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the...

We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for general admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes. 1.Introduction. In our paper Delbaen and Schacherma...

Let {Xi}i≥1 be a martingale difference sequence with Xi = Si − Si−1. Under some regularity conditions, we show that (X 1+· · ·+X2 Nn)SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided. Keywords—central limit theorem...

Abstract The main purpose of this article is to study the symmetric martingale property and capacity defined by G-expectation introduced by Peng (cf. http://arxiv.org/PS_cache/math/pdf/0601/ 0601035v2.pdf) in 2006. We show that the G-capacity can not be dynamic, and also demonstrate the relationship between symmetric G-martingale and the martingale under linear expectation. Based on these resul...